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

 

[Nickie]

I would approach this problem by breaking it down into smaller parts and using the principles of projectile motion and relative velocity to analyze the situation.

First, I would consider the motion of the first tank, which is firing the projectile. The projectile will follow a parabolic path due to gravity, and its horizontal velocity will remain constant at 250m/s. Using the equation y=yo+voy*t+1/2*a*t^2, I can calculate the time it takes for the projectile to hit the ground if the tanks were both stationary (8.85 seconds, as you have correctly calculated).

Next, I would consider the motion of the second tank. It is retreating at a speed of 35m/s relative to the ground, but since the first tank is also moving at a speed of 15m/s, the relative velocity between the two tanks is 35m/s + 15m/s = 50m/s. This means that the second tank is effectively moving away from the projectile at a speed of 50m/s.

Now, I can use the concept of relative velocity to determine the horizontal distance between the tanks when the projectile was first fired. Since the projectile takes 8.85 seconds to hit the ground, the second tank will have traveled a horizontal distance of 50m/s * 8.85s = 442.5 meters in that time. This means that the tanks were 442.5 meters apart when the projectile was first fired.

In conclusion, by considering the motion of the projectile and the relative velocity between the two tanks, we can determine the distance between the tanks when the round was first fired. This problem highlights the importance of understanding both projectile motion and relative velocity in analyzing real-world situations.