Chapter 4.8, Problem 17P

To determine

To find how long will it be before the flare passes the balloonist again on the way down?

Answer to Problem 17P

In 40 seconds the flare passes the balloonist.

Explanation of Solution

Given information: A signal flare is fired upward from ground level with an initial speed of 294m/s. A balloonist cruising at a height of 2450m.

Calculation: The required solution is obtained as,

Use the projectile equation, $h=vt-4.9t^2$ .

Velocity , $v=294m/s$

Height , $h=2450m$

  $\begin{array}{l}h=vt-4.9t^2\\ 2450=294t-4.9t^2=0\\ 4.9t^2-249t+2450=0\\ t^2-60t+500=0\\ \left(t-10\right)\left(t-50\right)=0\\ t=10,50\end{array}$

The flare passes the balloonist 10 seconds after it fired and continuous upwards. It reaches its maximum height and returns to the ground, passing the balloonist again 50 seconds after it is fired . There is a difference of 40 seconds in between the two times the flare passes the balloonist.

Hence, in 40 seconds the flare passes the balloonist.