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

Answer:

  t = 1.099 s

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

$y = u t + \dfrac{1}{2}at^2$

$-3.16 = 2.51 t + \dfrac{1}{2}\times (-9.8)t^2$

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

using quadratic formula to solve the equation

$t = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

$t = \dfrac{-(-2.51)\pm \sqrt{2.51^2-4(4.9)(-3.16)}}{2\times 4.9}$

  t = 1.099 s, -0.586 s

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