Question

Adam drops a ball from rest from the top floor of a building at the same time Bob throws a ball horizontally from the same location. Which ball hits the ground first? (Neglect any effects due to air resistance.) They both hit the ground at the same time. Adam's ball Bob's ball It depends on how fast Bob throws the ball. It depends on how fast the ball falls when Adam drops it.

Answer 1

Both balls hit the ground at the same time

Step-by-step explanation:

Adam drops the ball from rest, so the ball just "falls" in vertical direction, being gravity its only acceleration, for cinematic movements we use that:

`y(t)=y_(0)+v_(0y)t+(1)/(2)gt^(2)`

In this case we have that gravity is negative, and as Adam drops the ball,
`v_(0y)=0`

Bob throws the ball horizontally, so the movement will be a parabola, we can divide into horizontal direction, and vertical direction.

But we only need to analize the vertical movement, in wich again the only acceleration is gravity, and compare it with Adam's ball. Again we have that gravity is negative, and as the initial throw is horizontal,
`v_(0y)=0`

Finally, we have that

`y(t)=h-(1)/(2)gt^(2)`

where

`h=y_(0)`

both for Adam's vertical drop, and for Bob's vertical component of the parabolic throw.

Now, if we put
`y(t)=0` (the origin of the vertical coordinate), we get for both cases that

`h=(1)/(2)gt^(2)`

where we can clear the value for the time t, of the fall, wich will be the same in both cases.

Hence, both balls hit the ground at the same time.