# Where does the rocket land relative to the cart?

• Remulak
In summary, the rocket goes up to a height of 81.8 meters before coming back down and landing about 122 meters from 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?

Last edited:
What numbers did you get?

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.

Last edited:
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...

Got 'em thank you

## 1. How does the weight of the rocket affect where it lands relative to the cart?

The weight of the rocket does not have a significant effect on where it lands relative to the cart. Other factors such as the initial velocity, angle of launch, and air resistance have a greater impact on the landing location.

## 2. Does the distance between the rocket and the cart at launch affect where the rocket will land?

Yes, the distance between the rocket and the cart at launch will have an impact on the landing location. The closer the rocket is to the cart at launch, the closer it will land to the cart.

## 3. Will the landing location of the rocket always be in the same place relative to the cart?

No, the landing location of the rocket will vary depending on the initial conditions such as velocity and angle of launch. It is possible for the rocket to land in a different location relative to the cart each time.

## 4. Can the rocket land in front of the cart?

Yes, the rocket can land in front of the cart if it is launched at a high enough velocity and angle. However, this is less likely to occur compared to the rocket landing behind the cart due to the force of gravity.

## 5. What role does air resistance play in determining where the rocket will land relative to the cart?

Air resistance can have a significant impact on the landing location of the rocket relative to the cart. The higher the air resistance, the more likely the rocket will land closer to the cart due to the deceleration caused by air resistance.

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