Question

A ball is dropped from a bridge $122.5\,m$ 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 $t s$.
For first ball
$S =u t+\frac{1}{2} a t^{2} $
$122.5 =0+\frac{1}{2} \times 9.8 \times t^{2}=4.9 a t^{2} $
$t =\sqrt{\frac{122.5}{4.9}}=\sqrt{25}=5\, s$
For second ball,
$122.5 =u(5-2)+\frac{1}{2} \times 9.8 \times(5-2)^{2} $
$=3 u+44.1 \Rightarrow 3 u=122.5-44.1$
$3 u =78.4 \Rightarrow u=26.1 \,m / s$