Projectile rock hitting a moving van problem

[N_L_]

I have equations for the following problem and an answer, but I am not sure if they are correct:

Suzie (a geology student) is attacking a police van during a demonstration for peace and love at the University. The van is escaping at 3.2 m/s. Suzie throws her rock when the back of the van is 5.0 meters away. The rock leaves her hand at 1.6 meters above the ground, with a speed of 9.0 m/s and an angle of 37 degrees above the horizon. The rock hits and dents the back door of the van. Find the position of the van (relative to Suzie) when the rock hits it. Also find the height of the rock when it hits the van.

Truck:
Xf = Xi + Vo*t + .5 a*t^2
Xf = 5 + 3.2 t + 0

Rock:
Vxf = Vxi = 7.19 m/s after breaking 9.0 m/s at 37 degrees down into x and y components

Xf = Xi + Vxo * t
Xf = 7.19*t

Vyf = Vyo - gt
Vyf = 5.42 - 9.8 t

Yf = Yo + Vyo * t - 4.9 t^2
Yf = 1.6 + 5.42 (1.25) - 4.9 (1.25)^2

The answers I got:

time = 1.25 seconds
Xf relative to Suzie = 9.01 meters
Vf = .7 m above the ground

Is there a mistake?

 

[topsquark]

I haven't checked the numbers but the method looks ok.

-Dan

 

[kyle8921]

I cannot confirm if your equations and answers are correct without seeing your calculations and assumptions. However, I can provide some feedback and suggestions on how to approach this problem.

Firstly, it is important to clearly define the coordinate system being used. In this case, it seems like the x-axis is parallel to the ground and the y-axis is perpendicular to the ground, with positive direction being upwards. It would be helpful to explicitly state this in your equations.

Next, make sure to use consistent units throughout your calculations. In this problem, it seems like you are using meters for distance and seconds for time, which is correct. However, make sure to also use meters per second for velocity and meters per second squared for acceleration.

In terms of your equations, it looks like you are using the correct kinematic equations for both the truck and the rock. However, it is important to note that the initial velocity of the rock is not 9.0 m/s, as it is thrown at an angle of 37 degrees. You will need to use trigonometry to determine the x and y components of the initial velocity.

Additionally, when finding the final position of the rock, you will need to add the x and y components separately, as they are moving in different directions. Similarly, when finding the final velocity of the rock, you will need to combine the x and y components using vector addition.

Lastly, when determining the position of the van and the height of the rock when it hits, make sure to take into account the initial position of the van and the height of the rock when it is thrown.

Overall, it is important to carefully review your calculations and make sure they are accurate and consistent. If you are still unsure, it may be helpful to consult with a physics or math tutor for further assistance.