A ball is dropped from top of a tower of 100 m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of 50 m / s. They will cross each other after (g=10 m / s 2)

Question

A ball is dropped from top of a tower of 100 m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of 50 m / s. They will cross each other after (g=10 m / s 2) (A) 1 s (B) 2 s (C) 3 s (D) 4 s

Tardigrade Admin · Accepted Answer

Let the two balls cross each other after time

t

.
Height covered by first ball

h_{1} = \frac{1}{2} g t^{2}

Height covered by second ball

h_{2} = u t - \frac{1}{2} g t^{2}

but

h_{1} + h_{2} = 100

\frac{1}{2} g t^{2} + u t - \frac{1}{2} g t^{2} = 100

u t = 100

50 \times t = 100

\Rightarrow t = 2 s

Q. A ball is dropped from top of a tower of 100m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of 50m/s. They will cross each other after (g=10m/s2)

1 s

2 s

3 s

4 s

Let the two balls cross each other after time t. Height covered by first ball h1​=21​gt2 Height covered by second ball h2​=ut−21​gt2 but h1​+h2​=100 21​gt2+ut−21​gt2=100 ut=100 50×t=100 ⇒t=2s

Q. A ball is dropped from top of a tower of $100 m$ height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of $50 m / s$ . They will cross each other after $(g = 10 m / s^{2})$