Question

A hot-air balloon is rising upward with a constant speed of 2.51 m/s. When the balloon is 3.16 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground

Answer 1

t = 1.099 s

Step-by-step explanation:

given,

constant speed = 2.51 m/s

height of balloon above ground = 3.16 m

time elapsed before it hit the ground = ?

Applying equation of motion to the compass

`y = u t + (1)/(2)at^2`

`-3.16 = 2.51 t + (1)/(2)* (-9.8)t^2`

`4.9 t^2 - 2.51 t - 3.16 = 0`

using quadratic formula to solve the equation

`t = (-b\pm √(b^2-4ac))/(2a)`

`t = (-(-2.51)\pm √(2.51^2-4(4.9)(-3.16)))/(2* 4.9)`

t = 1.099 s, -0.586 s

hence, the time elapses before the compass hit the ground is equal to 1.099 s.