Two balls are dropped to the ground from different heights. One ball is dropped 2 s after the other but they both strike the ground at the same time. If the first ball takes 5 s to reach the ground, then the difference in initial heights is (g=10ms-2)

Question

Two balls are dropped to the ground from different heights. One ball is dropped 2 s after the other but they both strike the ground at the same time. If the first ball takes 5 s to reach the ground, then the difference in initial heights is (g=10ms-2)  (A) 20 m (B) 80 m (C) 170 m (D) 40 m

Tardigrade Admin · Accepted Answer

s1=(1/2)gt12=(10/2)× (5)2=125 m s2=(1/2)gt22=(10/2)× (3)2=45 m ∴ s1-s2=125-45=80 m

Q. Two balls are dropped to the ground from different heights. One ball is dropped $2 s$ after the other but they both strike the ground at the same time. If the first ball takes $5 s$ to reach the ground, then the difference in initial heights is $(g = 10 m s^{- 2})$

20 m

80 m

170 m

40 m

160 m

$s_{1} = \frac{1}{2} g t_{1}^{2} = \frac{10}{2} \times (5)^{2} = 125 m$
$s_{2} = \frac{1}{2} g t_{2}^{2} = \frac{10}{2} \times (3)^{2} = 45 m$
$∴$ $s_{1} - s_{2} = 125 - 45 = 80 m$

Q. Two balls are dropped to the ground from different heights. One ball is dropped 2s after the other but they both strike the ground at the same time. If the first ball takes 5s to reach the ground, then the difference in initial heights is (g=10ms−2)