Question

A balloon ascends vertically with a constant speed
for 5 seconds, when a pebble falls from it reaching
the ground in 5 s. The speed of the balloon is
(1) 10 ms -1
(2) 12.5 ms
(3) 25 ms
(4) 15 ms -1​

Answer 1

Given

A pebble falls from a balloon in 5 seconds which has been traveling for 5 seconds with a constant velocity upwards.

To find

Speed of the balloon

Solution

Distance covered by the pebble is $s=vt\\\Rightarrow s=5v$

The speed of the balloon will be the same as that of the pebble but their directions will be opposite so

$u=-v$

t = Time taken = 5 s

g = Acceleration due to gravity = $10\ \text{m/s}^2$

From the kinematic equations we get

$s=ut+\dfrac{1}{2}gt^2\\\Rightarrow 5v=-v5+\dfrac{1}{2}\times 10\times 5^2\\\Rightarrow 10v=125\\\Rightarrow v=\dfrac{125}{10}\\\Rightarrow v=12.5\ \text{m/s}$

The speed of the balloon is (2) 12.5 m/s.