Two tanks(Projecctile Motion and Relatve Velocity)

[Toranc3]

Homework Statement

Two tanks are engaged in a training exercise on level ground. The first tank fires a paint-filled training round with a muzzle speed of 250m/s at an angle 10.0 degrees above the horizontal while advancing toward the second tank with a speed of 15m/s relative to the ground. The second tank is retreating at a speed of 35m/s relative to the ground, but is hit by the shell. You can ignore air resistance and assume the shell hits at the same height above ground from which it was fired


Find the distance between the tanks when the round was first fired

Homework Equations

y=yo+voy*t+1/2*a*t^(2)

The Attempt at a Solution

Made my origin where tank 1 is at with positive going up and right. I am not too sure how to go about this though. I solved for the time it takes the projectle to hit the retreating tank. However that is if the tanks were both stationary but they are not.

Time it takes for shell to hit the retreating tank if they were both stationary:

y=yo+voy*t+1/2*a*t^(2)
0=0+250m/s*sin(10)*t-1/2*g*t^(2)
-250m/s*sin(10)*t=-1/2*g*t^(2)
t=8.85 seconds

I am stuck here.I know that I am going to have to use relative velocity but I am not sure how to connect it all together. Could somebody point me in the right direction?

 

[LawrenceC]

Your time if flight is correct. Now determine how far the projectile travels horizontally in that amount of time realizing that the target tank has also moved a distance in the same amount of time. The projectile horizontal velocity is greater than 250*cos(10).

 

[Toranc3]

Your time if flight is correct. Now determine how far the projectile travels horizontally in that amount of time realizing that the target tank has also moved a distance in the same amount of time. The projectile horizontal velocity is greater than 250*cos(10).

Thanks for the help! I will post up my work soon so you can check it if that is ok with you. Thanks again!

 

[Toranc3]

Hey why is it wrong to calculate the horizontal distance with the velocity of the shell relative to tank 1? Why must if be the velocity of the shell relative to the earth