TBR Translational Motion Review Question 7

[soccatrini08]

---

Members don't see this ad.

The passage describes a scenario in which three balls of equal mass are launched from a cannon at the same speed (50 m/s) but at different angles (0, 30, and 60 degrees). Question 7 asks which of the following balls hits the ground with the greatest kinetic energy. The answer is that all of them hit the ground with the same kinetic energy. Their reasoning is that all the balls have the same initial and final PE and same initial KE, as they all start from the same height and end at the same height.

(PE + KE)final = (PE + KE)initial

I'm confused because intuitively this doesn't make sense to me. Even though they start at the same height and finish at the same height, the balls don't hit the ground with the same velocity, which should affect their final KE based on the equation KE = 1/2 mv^2. No?

 

[farnell]

The balls actually do have the same velocity no matter what angle they are launched from. Though the angle will change the vertical and horizontal velocities, the vector sum will always be 50 if there are no other forces acting. Try drawing out the x and y components of velocity to prove this to yourself.

 

[soccatrini08]

The balls actually do have the same velocity no matter what angle they are launched from. Though the angle will change the vertical and horizontal velocities, the vector sum will always be 50 if there are no other forces acting. Try drawing out the x and y components of velocity to prove this to yourself.

I forgot to mention that the cannon is on a cliff, so wouldn't that make a difference? The ball launched from a 60 degree angle will have a higher apex and have more time to fall and gain velocity than the 30 degree angle ball, no?

 

[farnell]

The situation still stays the same. The path with the higher apex has a smaller horizontal velocity so the resultant velocity vector will stay constant at whatever angle. Compare shooting the balls straight up 90 degrees and falling below the cliff with shooting the ball straight out at an angle of 0. You will see that the resulting vector is constant. Hope this helps