First slide

Release from certain height

Question

A ball is dropped from a bridge 122.5 metres above a river. After the ball has been falling for two seconds, a second ball is thrown straight down after it. What must its initial velocity be so that both hit the water at the same time

Moderate

A

49 m/sec
B

55.5 m/sec
C

26 .1 m/sec
D

9.8 m/sec

Solution

Let f be the time of fall of the first ball to reach the water.
Using the formula
$s = ut + \frac{1}{2} {gt}^{2}$ , we have
$122 \cdot 5 = 0 + \frac{1}{2} \times 9 \cdot 8 \times t^{2}$
Solving, we get t² = 25 or t = 5 sec
For the second ball, t = 5 - 2 = 3 sec
$122 \cdot 5 = u \times 3 + \frac{1}{2} \times 9 \cdot 8 \times (3)^{2}$
Solving it, we get u = 26 .1 m/sec

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