Question

A ball is dropped from a balloon going up at a speed of 7 m/sec. If the balloon was at a height 60m at the time of dropping the ball, how long will the ball take to reach the ground?

Answer 1

Task. A ball is dropped from a balloon going up at a speed of 7 m/sec. If the balloon was at a height $h_{0}=60\,m$ at the time of dropping the ball, how long will the ball take to reach the ground?

Solution. There is a gravitation force acting on a ball so that it moves with a constant acceleration $g=9.8~{}m/s^{2}$. The initial velocity of the ball is $v_{0}=-7~{}m/s$, so it is opposite to the acceleration. Therefore the height of the ball at time $t$ is given by the following formula:

$h(t)=h_{0}+v_{0}t-\frac{gt^{2}}{2}.$

We should find time $t$ when $h(t)=0$, so we obtain the following equation:

$60+7t-\frac{9.8t^{2}}{2}=0,$

$4.9t^{2}-7t-60=0,$

$D=(-7)^{2}-4*4.9*(-60)=1225=35^{2}$

$t_{1}=\frac{7+35}{2*4.9}=4.29~{}s,\qquad t_{2}=\frac{7-35}{2*4.9}=-2.86~{}s<0.$

Thus only the first solution is admissible, and so $t=4.29$ s.