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A spacecraft is traveling with a velocity of $v_{0 x}=5480 {m} / {s}$ along the $+x$ direction. Two engines are turned on for a time of 842 s. One engine gives the spacecraft an acceleration in the $+x$ direction of $a_{x}=1.20 {m} / {s}^{2}$ while the other gives it an acceleration in the $+y$ direction of $a_{y}=8.40 {m} / {s}^{2}$ At the end of the firing, find (a) $v_{x}$ and $({b}) v_{y}$

6490$m / s$7070$m / s$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

Hope College

Lectures

04:01

2D kinematics is the study…

10:12

A vector is a mathematical…

03:00

On a spacecraft, two engin…

04:02

Useful background for this…

05:33

A space vehicle is coastin…

01:15

A spaceship is traveling a…

03:19

A spacecraft is launched f…

05:11

Two rockets are flying in …

01:30

A rocket is fired from res…

A rocket has total mass $M…

06:51

A 2 -kg model rocket is la…

03:16

A spacecraft descends vert…

04:36

A 2540 -kg test rocket is …

03:55

A 2540-kg test rocket is l…

00:11

A rocket is fired at an an…

02:03

Two rockets are launched a…

09:21

Determine the distance tra…

12:38

09:40

The rocket used to launch …

08:08

A faulty model rocket move…

03:37

A model rocket is launched…

All right, We're gonna do problem 12 here in this video. So first things first, it's right down. The question gives us the question says that we have a velocity in the ex direction on Lee V zero X It gave us to it as the not X as 5480 meters per second. Okay. And then give us ah, changing time. So the change in time of what those engines were on was 842 seconds. So before the engines turned on, it was going this this fast in the ex direction and then two engines turn on for 842 seconds. One accelerates the ship in the ex direction at 1.20 meters per second squared. The other one pushes it in the wind direction at 8.40 meters per second squared. So part, eh, once Ah, thing was, it wants the velocity and the ex direction after the engines turn on and then for part to be it wants. How fast going Why So mr a new page here. So this is part Hey, So first off, we know that like we have an initial velocity. What we call the zero is able to 5480 meters per second. Okay, Perfect. And then we know the formula. Acceleration equals velocity over time or change in velocity over time. So if we want to play, if we want to rearrange for changing velocity, we just want to play. So, uh, change in velocity equals time, Times acceleration. So we have a change in time. So our delta T is 842 seconds and our X acceleration acceleration and her X is equal to 1.20 meters per second squared. So we have all the variables need we need now toe self for a change in velocity. So are changing Velocity equals 842 seconds times acceleration of 1.20 meters per second squared. And that delta V is 1000 and 10.4 meters per second as a change. But we're not done because this with their initial velocity And then the jets turned on, which made us go that much faster. So now we have to add these two here to get our final velocity in the ex direction. So v sub zero plus change in velocity is equal to the velocity and extraction of our spaceship was in total. So 5480 meters per second plus 1000 and 10.4 meters per second is equal to, um 6000 490.4 meters per second in the extraction. So we just found this is our final velocity and the extraction out for those jets have been pushing that ship. Yeah, perfect. So now we can go on a party and we can find the wife. So, Adam, your page and this is going to be part B. So, um does it We have so notice how we have no initial velocity and the Y direction on Lee going in the axe. That means when our jets turn on the why when our engines turned on, it's gonna accelerate us in the wider action. We're not gonna have to add anything onto it like we had to in the last questions. It was just purely for what we did in the last question. Change in velocity equals acceleration, times time, and it gives us a Y acceleration of 8.40 meters per second squared and changing time of 842 seconds. So from multiplying most to you, together we get 7072.8 meters per second. Now for the purpose of these questions, with significant digits being a factor, we have to go round our answers. So if a part a our answer is really, uh, 6490 meters per second. And for part B, it's 7070 meters per second and those air to final answers for those two problems. Thanks for watching and hope this video is hopeful.

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