Question

A ball is dropped from a balloon going up at a speed of 5 m/s. If the balloon was at a height 60 m. at the time of dropping the ball, how long will the ball take to reach the ground? (Ans: 4s)

Answer 1

Given conditions ⇒

Initial Speed of the ball(u) = -5 m/s.

[Since, ball is dropped from the balloon].

Height of the balloon = 60 m.

Acceleration due to gravity = 9.8 m/s²

Using the Formula,

S = ut + 1/2at²

⇒ 60 = -5t + 1/2 × 9.8 × t²

⇒ 60 = -5t + 4.9t²

⇒ 4.9t² - 5t - 60 = 0

∴ 49t² - 50t - 600 = 0

This is th quadratic equation. If we solve it by the methods of the quadratic Formula,

we wlil get, t = - 4.02 and t = 3.03 seconds.

Since, time cannot be negative. Hence time will be 3 seconds.

Hence, the time taken by the ball is 3.02 seconds.

Hope it helps.