Chapter 4.8, Problem 19P

To determine

To find how much farther will it travel upward before starting to fall back to the ground ?

Answer to Problem 19P

3062.5m will it travel upward before starting to fall back to the ground.

Explanation of Solution

Given information: A rocket is moving vertically upward with speed 245m/s.

Calculation: The required solution is obtained as,

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

Velocity , $v=245m/s$ .

Set the zero height at when the fuel runs out. $h=0$

  $\begin{array}{l}h=vt-4.9t^2\\ 0=245t-4.9t^2\\ 0=t\left(245-4.9t\right)\\ t=0,50\end{array}$

Since the rocket goes up, then back down, without any power, the maximum height is found at the time that is half the total trip.

  $t_m=\frac{50-0}{2}=25$

Substitute the halfway time into the vertical motion equation to find the height.

  $\begin{array}{l}h=vt-4.9t^2\\ =245\left(25\right)-4.9{\left(25\right)}^2\\ =6125-3062.5\\ =3062.5\end{array}$

Hence, 3062.5m will it travel upward before starting to fall back to the ground.