Why do objects thrown from a cliff hit the ground at the same speed?

[samona]

Homework Statement

two balls are thrown from a cliff. one is thrown directly up, the other directly down, each with the same initial speed, and both hit the ground below the cliff. which ball hits the ground at the greater speed?

The Attempt at a Solution

I know the answer is that they both his the ground at the same speed. But why?

 

[Curious3141]

Homework Statement

two balls are thrown from a cliff. one is thrown directly up, the other directly down, each with the same initial speed, and both hit the ground below the cliff. which ball hits the ground at the greater speed?

The Attempt at a Solution

I know the answer is that they both his the ground at the same speed. But why?

This is only true when drag from the air is neglected, btw.

Consider conservation of energy. For each ball, PE + KE is a constant. Think about what happens to the ball thrown upward. What is its speed at the instant when it comes back downward to pass the point it was thrown from?

 

[samona]

When it returns to the position it started out as, then the velocity should equal the initial velocity.

 

[Curious3141]

When it returns to the position it started out as, then the velocity should equal the initial velocity.

Careful there. When it was thrown upward, its direction was upward. When it comes back down, its direction is reversed. Since velocity is a vector with both magnitude and direction, you can't say the final velocity equals the initial velocity. You can, however, say that the final speed equals the initial speed.

So the ball comes back down with the same speed it was thrown up at. Now its velocity (both magnitude and direction) is the same as the second ball that was thrown downward from the start. Can you immediately see the rest of the way to the solution?

 

[samona]

Got it! Thank you!

 

[Curious3141]

You're welcome.