3. How long will it take a ball to reach the ground if it falls from a cliff 25 m tall (starting from rest)? What if the ball we
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Answer:
Approximately . (Assuming that the drag on this ball is negligible, and that
.)
Explanation:
Assume that the drag (air friction) on this ball is negligible. Motion of this ball during the descent:
- Horizontal: no acceleration, velocity is constant (at
is constant throughout the descent.)
- Vertical: constant downward acceleration at
, starting at
.
The horizontal velocity of this ball is constant during the descent. The horizontal distance that the ball has travelled during the descent is also given: . Combine these two quantities to find the duration of this descent:
.
In other words, the ball in this question start at a vertical velocity of , accelerated downwards at
, and reached the ground after
.
Apply the SUVAT equation to find the vertical displacement of this ball.
.
In other words, the ball is below where it was before the descent (hence the negative sign in front of the number.) The height of this cliff would be
.