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A motorboat is racing towards the north at 25 $km{h^{ - 1}}$and the water current in that region is 10$km{h^{ - 1}}$in the direction of ${60^0}$east of south. The resultant velocity of the boat is: A. 11$km{h^{ - 1}}$ B. 22$km{h^{ - 1}}$ C. 33$km{h^{ - 1}}$ D. 44$km{h^{ - 1}}$

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• A motorboat is racing towards ...

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• A motorboat is racing towards north at 25 km h-1 and the water current in that region is 10 km h-1 in the direction of 60° east of south. The resultant velocity of the boat is

Q. A motorboat is racing towards north at 25 km h − 1 and the water current in that region is 10 km h − 1 in the direction of 6 0 ° east of south. The resultant velocity of the boat is

11 km h − 1, 22 km h − 1, 33 km h − 1, 44 km h − 1, the velocity of the motor boat and the velocity of the water current are represented by vectors v b ​ and v c ​ as shown in the figure. here, θ = 18 0 ° − 6 0 ° = 12 0 ° v b ​ = 25 km h − 1 , v c ​ = 10 km h − 1 ∴ according to parallelogram law of vector addition, the magnitude of the resultant velocity of the boat is v r ​ = v b 2 ​ + v c 2 ​ + 2 v b ​ v c ​ cos 12 0 ° ​ = ( 25 ) 2 + ( 10 ) 2 + 2 ( 25 ) ( 10 ) ( 2 − 1 ​ ) ​ = 625 + 100 − 250 ​ ≈ 22 km h − 1.

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A motorboat is racing towards north at 25 kmph and the water current n that region is 10 kmph in the direction of 60 0  east of south. The resultant speed of the boat is

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Correct option is A

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A motorboat is racing towards north at 25 km/h and the water current in that region is 10 km/h in the direction of 60 ∘ east of south. The resultant velocity of the boat is

The correct option is b 22 km/hr , at an angle tan − 1 ( 0.433 ) east of north. the vector v b representing the velocity of the motorboat and the vector v c representing the water current are shown in the figure in directions specified by the problem. using the parallelogram method of addition, the resultant r is obtained in the direction shown in the figure. so, the magnitude of the resultant is given by r = √ v 2 b + v 2 c + 2 v b v c cos θ , where θ = 120 ∘ ⇒ r = √ 25 2 + 10 2 + 2 × 25 × 10 cos ( 120 ∘ ) r = 21.8 ≈ 22 km/hr now, for direction we have tan ϕ = v c sin ( 120 ∘ ) v b + v c cos ( 120 ∘ ) = 10 sin ( 120 ∘ ) 25 + 10 cos ( 120 ∘ ) ⇒ tan ϕ = 0.433 ⇒ ϕ = tan − 1 ( 0.433 ) east of north..

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‘History doesn’t repeat itself:’ Northwestern experts on the DNC and a sprint to Election Day

• Expert Viewpoint

It’s a pivotal moment for the Democratic Party as nominees, delegates and more descend on Chicago for the 2024 Democratic National Convention (DNC).

The convention closes out a politically eventful summer that included the attempted assassination of former President Donald Trump and President Joe Biden ending his bid for reelection and endorsing Vice President Kamala Harris for the role. It also kicks off a sprint toward election day as both major parties continue to adjust to the new dynamics of the race and attempt to engage voters on key issues.

Here’s what Northwestern experts are saying about the DNC and other essential topics.

Why Black women will be an important voting bloc in this election  

Sally Nuamah, associate professor of political science, human development and social policy in the School of Education and Social Policy:

“General elections are often won with slight margins, for example in the 2016 election. So, the consistent and high participation of Black women is often what helps the Democrats secure close victories making their participation essential. Black women are also critical for organizing members of their own communities, including Black men and other racial groups as we see, for example, with Stacey Abrams in Georgia.”

Protests and the 1968 DNC

Heather Hendershot, professor of communication studies in the School of Communication:

“When the Democratic convention was held in Chicago in the summer of 1968, Mayor Richard J. Daley allowed his police force to beat and teargas protestors, journalists, and delegates, and Americans saw it all at home on TV. In the weeks that followed, Richard Nixon’s campaign hammered home the point that Americans could not expect Democrats to run the country if they could not even control their own convention, and that perception took root, helping Nixon to win in November. Similarly, if the Chicago streets boil over in violence next week, the Trump campaign will weaponize images of that violence (on Truth Social, Fox News, and elsewhere) against Democrats up and down the ballot. 

“And yet, the difference in police and City Hall leadership may make a huge difference this time around; this is crucial if the city is to avoid violence and the Democratic Party is to convey itself as the anti-authoritarian alternative to Trump’s GOP. Crucially, any street violence will appear not only on TV as it did in 1968 but also via social media. Crisis moments may be amplified. Even in the absence of violence, deep fakes and other sorts of deceptions are a real risk in today’s fragmented, erratic, and unpredictable media ecosystem.”

How the past can and can’t instruct us

Kevin Boyle, William Smith Mason Professor of American History and department chair in the Weinberg College of Arts and Sciences . From WTTW News :

“History doesn’t repeat itself. The past is most useful to us as a way of understanding how we got to where we are today, rather than seeing it as somehow being repeated. It’s about the roots of the life we live now, and I really do think there are serious roots in the late ’60s, ’68, and in the Nixon years that helped to create the world we live in now.”

AI and the increasing threat of political misinformation

Erik Nisbet, Owen L. Coon Endowed Professor of Policy Analysis & Communication and director of the Center for Communication & Public Policy in the School of Communication. From a DNC panel on the growing threat AI-driven disinformation with former Assistant Secretary of State Michael Posner:

“We know in battleground states, it’s going to be 50/50. Whoever wins, there will be a surge of misinformation and disinformation about the election results. AI is supercharging this, making videos more emotional and provocative while lowering the barriers to entry, allowing more people to get involved in high-impact disinformation events.”

Political violence in the wake of the Trump assassination attempt

Laurel Harbridge-Yong, professor of political science in the Weinberg College of Arts and Sciences and faculty fellow at the Institute for Policy Research. In the Chicago Sun-Times with the University of Illinois Chicago’s Alexandra Filindra, Paul Teas and Andrea Manning:

“Combined with research showing that what partisan leaders say about violence matters, our research suggests that exposure to stories of political violence does not drive partisans to view violence as justified. Instead, it may reduce support for violence as people come face-to-face with the true human cost of such events. However, this may depend on how trusted partisan leaders respond and whether they actively work to promote peaceful co-existence and denounce violence. Exercising restraint is key to the preservation of democratic institutions, and during this contentious election cycle, both citizens and leaders should heed that lesson.”

Trump’s attacks on Harris’s racial identity

  Tabitha Bonilla, associate professor of human development and social policy in the School of Education and Social Policy and research assistant professor at the Institute for Policy Research. In The Hill :

“Blackness isn’t just one thing, as is no identity. You can be multiple things at one time. But I think most conversations on race and ethnicity tend to fall flat and think about entire groups of people as though they were one thing, and that’s just factually incorrect.

“It also leads to a lot of harm in that it leaves out people who may not fit this modal standard of what we think their racial identity should be. It limits an individual’s ability to be wholly who they are and who they want to be.”

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PHYS Example 4.3 A motorboat is racing towards north at 25 km/h and the water current in that region is 10 km/h in the direction of 60° east of south. Find the resultant velocity of the boat. TO

A motorboat is racing towards the north at $ 25 km/h$ and the water current in that region is $ 10 km/h$ in the direction of $ 60°$ east of south. The resultant velocity of the boat is:

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Harris Puts Four Sun Belt States Back in Play, Times/Siena Polls Find

Kamala Harris and Donald Trump are in close races across Arizona, Georgia, Nevada and North Carolina, crucial swing states that Mr. Trump had seemed en route to run away with just a few weeks ago.

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The New York Times/Siena College Poll

Aug. 8 to 15

If the 2024 presidential election were held today, who would you vote for if the candidates were Kamala Harris and Donald Trump ?

North Carolina

Among likely voters. Shaded areas represent margins of error.

By Shane Goldmacher and Ruth Igielnik

Vice President Kamala Harris has stormed into contention in the fast-growing and diverse states of Arizona, Georgia, Nevada and North Carolina, not long after Donald J. Trump had seemed on the verge of running away with those states when President Biden was still the Democratic nominee.

The new polls from The New York Times and Siena College show how quickly Ms. Harris has reshaped the terrain of 2024 and thrust the Sun Belt back to the center of the battleground-state map.

Ms. Harris is now leading Mr. Trump among likely voters in Arizona, 50 percent to 45 percent, and has even edged ahead of Mr. Trump in North Carolina — a state Mr. Trump won four years ago — while narrowing his lead significantly in Georgia and Nevada.

Mr. Trump and Ms. Harris are tied at 48 percent across an average of the four Sun Belt states in surveys conducted Aug. 8 to 15.

That marks a significant improvement for Democrats compared with May, when Mr. Trump led Mr. Biden 50 percent to 41 percent across Arizona, Georgia and Nevada in the previous set of Times/Siena Sun Belt polls , which did not include North Carolina.

[A dead heat in these four states is not great news for Donald Trump, and it represents a huge shift from earlier in the cycle, Nate Cohn writes .]

The new polls provide more evidence that Ms. Harris is successfully consolidating parts of the Democratic base that had been waffling over supporting Mr. Biden for months, particularly younger, nonwhite and female voters.

Last week, Times/Siena polling showed that Ms. Harris had pulled ahead of Mr. Trump by a narrow margin in the three northern battleground states of Michigan, Pennsylvania and Wisconsin. Those states are generally considered the linchpin of any Democratic path to the White House. The Sun Belt represents an essential set of states for Mr. Trump while offering a potential second route for Ms. Harris to the 270 Electoral College votes needed to win.

In the new surveys, Mr. Trump is ahead in Georgia 50 percent to 46 percent, and, in Nevada, he has 48 percent compared to 47 percent for Ms. Harris. She has 49 percent of likely voters to Mr. Trump’s 47 percent in North Carolina, the only one of the seven core battleground states that he carried in 2020.

The polls show some risk for Ms. Harris as she rallies Democrats to her cause, including that more registered voters view her as too liberal (43 percent) than those who say Mr. Trump is too conservative (33 percent). For now, she is edging ahead of him among critical independent voters.

The new results come after as tumultuous a two-month period as there has ever been in modern American politics. Democrats swapped Ms. Harris for Mr. Biden after his poor debate performance, and, in between, Mr. Trump survived an assassination attempt and made a dramatic return at his party’s convention.

How the Times/Siena polls compare

Both parties view the current period as a potential inflection point and are pouring tens of millions of dollars into advertising in the swing states to shape voter perceptions as Democrats prepare to gather next week for their party convention in Chicago.

The polls show that Democratic voters are newly excited about the 2024 race now that Ms. Harris is the nominee, with 85 percent of her voters saying they are at least somewhat enthusiastic about voting this fall, roughly matching voters’ level of enthusiasm for Mr. Trump. And large majorities of Democratic and Republican registered voters are now satisfied with their choice of candidates. That is a marked change from May, when Republicans were much more satisfied than Democrats.

Alina Szmant, 78, a Democrat and a retired scientist in Wilmington, N.C., was excited about the possibility of voting for the first female president.

“Kamala is extremely well prepared to be an excellent president,” she said. As for Mr. Biden? She would have voted for him mostly because of her disgust for Mr. Trump. “He was not my first choice,” she said of Mr. Biden. “He wasn’t even my second or third or fourth choice.”

The race is increasingly polarized along racial lines.

Ms. Harris, who would be the first Black woman to serve as president, had the support of 84 percent of Black voters in the polls, which is higher than Mr. Biden’s support before his exit. Her backing among Latino voters was at 54 percent. She also opened up a significant gender gap, taking a 14-percentage point lead over Mr. Trump among women in Arizona, Georgia and Nevada; that group had been evenly split between Mr. Biden and Mr. Trump in those three states in May.

Overall, Ms. Harris leads nonwhite voters in Arizona, Georgia and Nevada by 29 percentage points; Mr. Biden had led those voters in the same states by 17 percentage points in May.

Mr. Trump, in turn, is maximizing his support among white voters without a college degree, winning 66 percent support from them across the four Sun Belt states.

One of the bigger questions for Ms. Harris is how long what the Trump team has called her “honeymoon” period will last. She has sparked memes, become a social-media phenomenon and drawn larger crowds on her first trip across the swing states last week than Mr. Biden ever drew.

One indicator of her online traction came from largely younger voters who said they used TikTok. Ms. Harris held a 13-point advantage among TikTok users in Arizona, Georgia and Nevada, compared with Mr. Biden’s 3-point edge among the same group in those states in May.

Voters overall gave Ms. Harris a 48 percent favorable rating, the same as her unfavorable rating. No previous Times/Siena survey in these states tested her favorability, but an even rating is a huge leap. In one national survey in February , voters viewed her more unfavorably by a 19-percentage point margin.

Mr. Trump scored an identical 48 percent favorable rating, largely unchanged since May.

[Follow the latest polls and see updated polling averages of the Harris vs. Trump matchup .]

The relative good will from the electorate for both candidates is a significant change from earlier in the year, when many frustrated voters described a Trump-Biden rematch with a mixture of disgust and disinterest.

“I was pretty nervous before,” said Freyja Brandel-Tanis, a 28-year-old urban planner in Atlanta who described herself as a “leftist.” But since Ms. Harris’s ascent, she said, “I think that the enthusiasm is definitely there.”

Still, there are already some warning signs of Ms. Harris’s potential vulnerabilities.

More voters said she flip-flops on issues that matter than said the same about Mr. Trump. The divide is particularly pronounced among Hispanic voters, who were 12 percentage points more likely to say Ms. Harris changes her positions on important issues than to say the same about Mr. Trump.

Mr. Trump also continues to hold the political advantage on two issues — the economy and immigration — that voters ranked as among the most important facing the nation. But Ms. Harris and Mr. Trump are close to tied on the key question of which candidate would better handle whatever issue voters see as the most important to them.

One reason is that while Mr. Trump is still favored on the economy over Ms. Harris across the Sun Belt states, his advantage is smaller on that topic than it was over Mr. Biden in May. At the same time, Ms. Harris has widened the Democratic edge over Mr. Trump on abortion.

On the issue of immigration, Mr. Trump is more trusted by 53 percent of voters, compared with 43 percent for Ms. Harris. Still, for an issue that has been a defining part of Mr. Trump’s image since 2015, that advantage represents a relatively small edge.

The state of the race in the four Sun Belt states was unchanged when third-party candidates were included. Robert F. Kennedy Jr. won just 4 percent of likely voters, the largest of any third-party candidate in the polls, but it is half the level of support he received in Arizona, Nevada and Georgia just three months ago.

As the Harris and Trump campaigns rush to define each other in the remade race, voters see a choice between strength and compassion.

Ariz., Ga., N.C., Nev.

Percentage of registered voters who said these traits described each candidate “very well” or “somewhat well”

Can unify the country

Cares about people like you

Flip-flops on issues that matter

Is a strong leader

Is qualified

Will bring about the right kind of change

Voters were about equally likely to see each candidate as qualified and change-makers, but significantly more voters viewed Mr. Trump as a strong leader. Ms. Harris is seen by more voters than Mr. Biden was as an agent of change, but, overall, voters still see Mr. Trump as the candidate who will shake things up.

When voters were asked who “cares about people like me,” Ms. Harris had a slight edge over Mr. Trump: 52 percent compared to 48 percent. Though about half of Hispanic voters said Mr. Trump cares about people like them, even more said the same about Ms. Harris.

Sergio Villavicencio, a 40-year-old Marine veteran who lives in Buckeye, Ariz., said he voted for Mr. Trump in 2016 and then switched to Mr. Biden in 2020. He is planning to support Ms. Harris now, partly because, he said, Ms. Harris seems more concerned about his issues.

“If that person’s supposed to be representing all of us, and he’s picking and choosing who he’s representing — billionaires and Elon Musk and all these kinds of corporations — like, he’s not speaking for the people,” Mr. Villavicencio said of Mr. Trump. “He’s not talking to the people. He doesn’t give a damn about the people.”

The brightening of the landscape for Democrats also applies lower down the ballot, where Senate races were polling stronger for the party than in May.

In Arizona, Ruben Gallego, the Democratic congressman, leads Kari Lake, the firebrand pro-Trump Republican and former television anchor, 51 percent to 42 percent, among likely voters in the state’s open Senate race. In Nevada, Senator Jacky Rosen, a Democrat, is ahead of her Republican challenger Sam Brown 49 percent to 40 percent. And in North Carolina, the state’s Democratic attorney general, Josh Stein, leads Lt. Gov. Mark Robinson, a Republican, 49 percent to 39 percent, in the year’s marquee governor’s race.

Camille Baker contributed reporting. Additional contributions by Christine Zhang .

Here are the key things to know about these Times/Siena polls:

Interviewers spoke with 677 registered voters in Arizona from Aug. 8 to 15; 661 registered voters in Georgia and 655 registered voters in North Carolina from Aug. 9 to 14; and 677 registered voters in Nevada from Aug. 12 to 15.

Times/Siena polls are conducted by telephone, using live interviewers, in both English and Spanish. More than 95 percent of respondents were contacted on a cellphone for these polls. You can see the exact questions that were asked and the order in which they were asked here .

Voters are selected for Times/Siena surveys from a list of registered voters. The list contains information on the demographic characteristics of every registered voter, allowing us to make sure we reach the right number of voters of each party, race and region. For these polls, interviewers placed more than 276,000 calls to nearly 183,000 voters.

To further ensure that the results reflect the entire voting population, not just those willing to take a poll, we give more weight to respondents from demographic groups that are underrepresented among survey respondents, like people without a college degree. You can see more information about the characteristics of respondents and the weighted sample at the bottom of the results and methodology page , under “Composition of the Sample.”

The margin of sampling error among registered voters is plus or minus 2.1 percentage points across the four states, plus or minus 4.1 percentage points in Arizona and Georgia, and plus or minus 4.2 percentage points in Nevada and North Carolina. In theory, this means that the results should reflect the views of the overall population most of the time, though many other challenges create additional sources of error. When computing the difference between two values — such as a candidate’s lead in a race — the margin of error is twice as large.

You can see full results and a detailed methodology here . If you want to read more about how and why we conduct our polls, you can see answers to frequently asked questions and submit your own questions here .

Shane Goldmacher is a national political correspondent, covering the 2024 campaign and the major developments, trends and forces shaping American politics. He can be reached at [email protected] . More about Shane Goldmacher

Ruth Igielnik is a Times polling editor who conducts polls and analyzes and reports on the results. More about Ruth Igielnik