Question

Two spherical balls having equal masses with a radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3 s with the same initial velocity of 35 m/s, then these balls collide at a height of ______ m.

(take g = 10 m/s²)

Options

• 30

• 40

• 50

• 20

Answer 1

Two spherical balls having equal masses with a radius of 5 cm each is thrown upwards along the same vertical direction at an interval of 3 s with the same initial velocity of 35 m/s, then these balls collide at a height of 50 m.

Explanation:

Two balls' displacements are

`S_1 = 35t - 1/2g t^2`

And `S_2 = 35(t - 3) - 1/2g(t - 3)^2`

⇒ S₁ = S₂ = h

⇒ `35t - (g t^2)/2 = 35(t - 3) - (g(t - 3)^2)/2`

⇒ `g/2[t^2 - (t - 3)^2] = 105`

⇒ `(2t - 3)(3) = 210/10`

⇒ 2t = 10 ⇒ t = 5 s

⇒ h = `35 xx 5 - 10/2 xx 25`

= 175 - 125

= 50 m