Question

Two balls P and Q are thrown vertically upwards from the ground at the same instant with speeds 20 m/s and 30 m/s respectively. Find the height (in m) of ball Q above the ground at the instant ball P is in air 20m below ball Q. [Take g = 10 m/s2]

Answer 1

Two balls P and Q are thrown vertically upwards from the ground at the same instant with speeds 20 m/s and 30 m/s respectively.

Let height of ball Q from the ground is h m.

so, height of ball P from the ground is (h - 20)m

for ball Q :

using formula, s = ut + 1/2 at²

here, s = h, a = -g = -10m/s² and u = 30m/s

so, h = 30t - 5t² .......(1)

for ball P :

using formula, s = ut + 1/2at²

here, s = (h - 20)m, a = -10m/s² and u = 20m/s

so, h - 20 = 20t - 5t² ......(2)

from equations (1) and (2),

20 = 10t => t = 2sec

and h = 30(2) - 5(2)² = 60 - 20 = 40m

hence, height of ball Q from the ground is 40m