Question

A balloonist releases a ballast bag from a balloon rising at 40 ms-1 at a time when the balloon is 100 m above the
ground. If g = 1@ms-2, then the bag reaches the ground in​

Answer 1

Answer:

The bag reaches the ground in 10 seconds.

Explanation:

Given:

• A balloonist releases a ballast bag from a balloon rising at 40 ms-1 at a time when the balloon is 100 m above the ground.
• Gravitational force (g) = 10 m/s².

To Find:

• The time when bag reaches the ground = ?

Solution:

We know that,

$\qquad {\red{\bf h = ut + \dfrac{1}{2} at^2}}$

$\implies \sf -100 = 40 + \dfrac{1}{2} \times (-g) t^2$

$\implies \sf - 100 = 40t \times \dfrac{1}{2} \times 10 t^2$

$\implies \sf 5t^2 - 40t - 100 = 0$

$\implies \sf t^2 - 8t - 20 = 0$

$\implies \sf t^2 - 10t + 2t - 20 = 0$

$\implies \sf t(t-10) + 2(t-10) = 0$

$\implies \sf (t - 10)(t + 2) = 0$

$\therefore {\large{\boxed{ \sf t = 10 sec}}}$

$\therefore$ The time when bag reaches the ground is 10 seconds.