Momentum before and after the collision and relative velocities.

[Jfex]

Homework Statement

If the truck was not stationary but was moving horizontally towards the ball at 25 ms-1, what would be the speed of the ball, relative to the ground, after the collision (in ms-1)?
Mass of ball = 0.2 kg
Mass of truck = 20 tonnes
Initial velocity of ball = 20 ms-1 (to the right)
Initial velocity of the truck = 25 ms-1 (to the left)
This is also a perfectly elastic collision

Homework Equations

P = mv

The Attempt at a Solution

So what I did first was equated the sum of the initial momentum's to the sum of the final momentum's to try and figure out what the final velocity of the ball was however it just gave me 20 which is incorrect.

so...

m₁v₁initial + m₂v₂initial = m₁v₁final + m₂v₂final

I found that because we can cancel the final and initial momentum's of the truck due to its change of velocity being negligible I can equate the initial and final momentum's of the ball. However when I do this it gives me a velocity of 20 which is still incorrect.

Thank you in advance.

 

[ehild]

The Attempt at a Solution

So what I did first was equated the sum of the initial momentum's to the sum of the final momentum's to try and figure out what the final velocity of the ball was however it just gave me 20 which is incorrect.

so...

m₁v₁initial + m₂v₂initial = m₁v₁final + m₂v₂final

I found that because we can cancel the final and initial momentum's of the truck due to its change of velocity being negligible I can equate the initial and final momentum's of the ball. However when I do this it gives me a velocity of 20 which is still incorrect.

Thank you in advance.

You can not ignore the change of momentum of the truck. The change of the velocity is small, but multiplied by the big mass, the magnitude is exactly the same as that of the change of momentum of the ball. Write up conservation of energy and use both equations to solve for the velocity of the ball.


ehild

 

[Jfex]

Sorry I'm not to sure how that will help because now I'm left with two variables; the final velocity of the final velocity of the ball?

0.2*20 + 20000*25 = 0.2*v_final + 20000*v_final

I'm not sure what you mean?

 

[ehild]

The collision is elastic. Use also the equation for conservation of energy.
Also, check the signs of the initial velocities. The ball and car move in opposite directions.

ehild