# Two tanks(Projecctile Motion and Relatve Velocity)

• Toranc3
In summary, Homework statement states that 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. The attempt at a solution states that the projectile horizontal velocity is greater than 250*cos(10).
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?

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

Last edited:

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.

## 1. How does projectile motion work in two tanks?

Projectile motion in two tanks is similar to projectile motion in any other scenario. The object (or projectile) follows a parabolic path due to the force of gravity, regardless of whether it is moving in one tank or two tanks. However, the presence of another tank can affect the trajectory of the projectile due to factors such as air resistance and collisions with the other tank.

## 2. What is the equation for calculating the distance traveled by a projectile in two tanks?

The equation for calculating the distance traveled by a projectile in two tanks is d = v0t + 1/2at2 where d is the distance traveled, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity. This equation can be used for both horizontal and vertical distances in two tanks.

## 3. How does relative velocity play a role in two tanks?

Relative velocity is the velocity of an object in relation to another object. In two tanks, relative velocity plays a role in determining the direction and speed of the projectile. The projectile's velocity in relation to one tank will affect its trajectory and behavior in the other tank, as well as the relative velocity between the two tanks.

## 4. Can the shape or size of the tanks affect the projectile's motion?

Yes, the shape and size of the tanks can affect the projectile's motion. For example, if one tank is taller than the other, the projectile may travel a greater vertical distance in that tank. Additionally, the shape of the tanks can create different air resistance and affect the projectile's trajectory.

## 5. How can you use two tanks to study projectile motion and relative velocity?

Two tanks can be used to study projectile motion and relative velocity by setting up different scenarios and observing how the projectile behaves in each tank. For example, changing the initial velocity, angle of launch, or placement of the tanks can provide insight into how these factors affect the projectile's motion. Additionally, using different objects of varying sizes and shapes can also be used to study the effects of relative velocity on the projectile.

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