Question

A ball is dropped from a bridge $122.5m$ above a river. After the ball has been falling for $2s$, a second ball is thrown straight down after it. What must the initial velocity of the second ball be so that both hit the water at the same time?

• A. 40 m/s
• B. 55.5 m/s
• C. 26.1 m/s
• D. 9.6 m/s

Answer 1

Answer: (C)

Let the ball hit water in $ts$.
For first ball
$S=ut+\frac{1}{2}a{t}^2$
$122.5=0+\frac{1}{2}\times 9.8\times t^2=4.9a{t}^2$
$t=\sqrt{\frac{122.5}{4.9}}=\sqrt{25}=5s$
For second ball,
$122.5=u(5-2)+\frac{1}{2}\times 9.8\times (5-2{)}^2$
$=3u+44.1\Rightarrow 3u=122.5-44.1$
$3u=78.4\Rightarrow u=26.1m/s$