Where does the rocket land relative to the cart?

[Remulak]

Homework Statement

Just started an introductory college physics I course. I'm interested in the course but I'm having a hard time grasping the concepts. I'm not great at math but you guys probably won't have a hard time with this problem. If somebody could help me that'd be great thanks.

A cart carrying a vertical rocket launcher moves horizontally at a constant velocity of 30.0 m/s to the right. It launches a rocket vertically upward with an initial speed of 40.0 m/s, as shown in the figure below. A) How high does the rocket go? B) How far does the cart travel while the rocket is in the air? C) Where does the rocket land relative to the cart? !
!
40.0 !
m/s 0 - Rocket
0
{---} ------------>
Cart 30.0 m/s

Homework Equations

y = yo + vt - 1/2gt^2
vy = vo - gt
x = xo + vt

The Attempt at a Solution

Okay so here's my thinking process, for part A, the rocket will be at its highest point when it's velocity is zero, vy = vo - gt, solve for t. Then plug t into y = yo + vt - 1/2gt^2, that should give me my final point in the y direction but I got it wrong. For Part B i thought you could take the t i found in Part A and plug it into x = xo + vt but I also got that wrong. Am I supposed to find the magnitude of the x and y vectors and find the angle?

 

[learningphysics]

What numbers did you get?

 

[Remulak]

Part A I got t = 4.07 seconds, and the height is 81.8 meters. Part B I got 122 meters for the car. I think I'm doing something wrong with my signs. I know this is definitely not right since the rocket is going 40m/s.

 

[learningphysics]

Yeah, you did the first part right but I get 81.6m not 81.8. The horizontal distance should be double what you've got because you need the time it takes to go up, and come back down... which is double the time it takes to go up.

But watch the decimal places... I'm not sure but I'm guessing that's why your first answer was not accepted.

only round at the very end...

 

[Remulak]

Got 'em thank you