Two tanks(Projecctile Motion and Relatve Velocity)

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The discussion revolves around a physics problem involving two tanks, one firing a projectile while the other retreats. The first tank fires a round at a speed of 250 m/s at a 10-degree angle, while the second tank moves away at 35 m/s. The original poster calculated the time for the projectile to hit the second tank under stationary conditions, yielding approximately 8.85 seconds, but is confused about incorporating relative velocities. The key point is that the horizontal distance must be calculated using the projectile's velocity relative to the ground, not just the first tank. Understanding this relative motion is crucial for determining the distance between the tanks at the moment of the projectile's impact.
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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?
 
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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).
 
LawrenceC said:
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!
 
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
 
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