Chapter 9.1, Problem 105E

(a)

To determine

To find:The equation of the parabolic path.

Answer to Problem 105E

The equation of the parabolic path is $x^2=-49\left(y-100\right)$ .

Explanation of Solution

Given information:

A ball is thrown from the top of a $100$ foot tower with a velocity of $28$ feet per second.

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 ball is thrown from a height of $100$ foot with a velocity of $28$ feet per second.

So, the value of $v$ is $28$ and value of $s$ is $100$ . Substitute these values in the formula.

  $\begin{array}{c}{x}^2=-\frac{v^2}{16}\left(y-s\right)\\ x^2=-\frac{{28}^2}{16}\left(y-100\right)\\ x^2=-49\left(y-100\right)\end{array}$

Therefore, the equation of the parabolic path is $x^2=-49\left(y-100\right)$ .

(b)

To determine

To calculate:The horizontal distance travelled by ball before striking the ground.

Answer to Problem 105E

The horizontal distance travelled by the ball before striking the ground is $70$ feet.

Explanation of Solution

Given information:

A ball is thrown from the top of a $100$ foot tower with a velocity of $28$ feet per second.

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:

As calculated in part(a), the equation of the parabolic path is $x^2=-49\left(y-100\right)$ .

Now to calculate the horizontal distance travelled by ball before striking the ground substitute $y=0$ in the parabolic path.

  $\begin{array}{c}{x}^2=-49\left(0-100\right)\\ x^2=4900\\ x=\pm 70\end{array}$

Therefore, the horizontal distance travelled by the ball before striking the ground is $70$ feet.