Chapter 9.1, Problem 102E

To determine

To find: The horizontal distance travelled by the crate before striking the ground.

Answer to Problem 102E

The horizontal distance travelled by crate before striking ground is $34294.6$ feet.

Explanation of Solution

Given information:

A cargo plane is flying at an altitude of $30000$ feet and speed of $540$ miles per hour. A supply crate is dropped from the plane.

Formula used:

The equation for the path is $x^2=-\frac{v^2}{16}\left(y-s\right)$ , where $v$ is the velocity and $s$ is the height, $y$ is the height of the projectile and $x$ is the horizontal distance the projectile travels.

Calculation:

The plane is flying at a height of $30000$ foot with a velocity of $540$ miles per hour.

As speed of $540$ miles per hour is equivalent to $792$ feet per second.

So, the value of $v$ is $792$ and value of $s$ is $30000$ . Substitute these values in the formula.

  $\begin{array}{c}{x}^2=-\frac{{792}^2}{16}\left(y-30000\right)\\ x^2=-39204\left(y-30000\right)\\ x^2=-49\left(y-100\right)\end{array}$

So, The equation of the parabolic path is $x^2=-39204\left(y-30000\right)$ .

Now to calculate the horizontal distance travelled by crate before striking ground substitute $y=0$ in the equation of the parabola.

  $\begin{array}{l}{x}^2=-39204\left(y-30000\right)\\ x^2=-39204\left(0-30000\right)\\ x^2=39204\left(30000\right)\\ x\approx 34294.6\end{array}$

Therefore, the horizontal distance travelled by crate before striking ground is $34294.6$ feet.