Chapter 6, Problem 52RE

(a)

To determine

To calculate: The altitude that the A’s parachute opens.

Answer to Problem 52RE

The altitude of A when the parachute open is 6144ft

Explanation of Solution

Given information:

Skydivers A and B are in a helicopter hovering at 6400 feet. The Skydiver A jumps and descends for 4 see before opening her parachute. The helicopter when climbs to 7000 feet and hovers there. Forty-?ve seconds after A leaves the aircraft. B jumps and descends for 13 sec before opening her parachute. Both skydivers descend at 16 ft/sec with parachutes open.

Formula used:

  $\left(\begin{array}{l}\text{Distance falling by A}\\ \text{before open the parachute}\end{array}\right)=\frac{1}{2}g{t}^2$

Calculation:

For free fall bodies

  $\begin{array}{l}\left(\begin{array}{l}\text{Distance falling by A}\\ \text{before open the parachute}\end{array}\right)=\frac{1}{2}g{t}^2\\ =\frac{1}{2}\left(32\right)\left(4^2\right)\\ =\frac{1}{2}\left(32\right)\left(16\right)\\ \left(\begin{array}{l}\text{Distance falling by A}\\ \text{before open the parachute}\end{array}\right)=256\text{ft}\end{array}$

Hence,

  $\begin{array}{l}\left(\begin{array}{l}\text{altitute of A when}\\ \text{parachute open}\end{array}\right)=6400-256\\ \left(\begin{array}{l}\text{altitute of A when}\\ \text{parachute open}\end{array}\right)=6144\text{ft}\end{array}$

Conclusion:

The altitude of A when the parachute open is 6144ft

(b)

To determine

To calculate: The altitude that the B’s parachute open.

Answer to Problem 52RE

The altitude of B when the parachute open is 4296ft

Explanation of Solution

Given information:

Skydivers A and B are in a helicopter hovering at 6400 feet. The Skydiver A jumps and descends for 4 see before opening her parachute. The helicopter when climbs to 7000 feet and hovers there. Forty-?ve seconds after A leaves the aircraft. B jumps and descends for 13 sec before opening her parachute. Both skydivers descend at 16 ft/sec with parachutes open.

Formula used:

  $\left(\begin{array}{l}\text{Distance falling by A}\\ \text{before open the parachute}\end{array}\right)=\frac{1}{2}g{t}^2$

Calculation:

For free fall bodies,

  $\begin{array}{l}\left(\begin{array}{l}DistancefallingbyB\\ \text{before open the parachute}\end{array}\right)=\frac{1}{2}g{t}^2\\ =\frac{1}{2}\left(32\right)\left({13}^2\right)\\ =\frac{1}{2}\left(32\right)\left(169\right)\\ \left(\begin{array}{l}DistancefallingbyB\\ \text{before open the parachute}\end{array}\right)=2704\text{ft}\end{array}$

Hence,

  $\begin{array}{l}\left(\begin{array}{l}\text{altitude of B when}\\ \text{parachute open}\end{array}\right)=6400-2704\\ \left(\begin{array}{l}\text{altitude of B when}\\ \text{parachute open}\end{array}\right)=4296\text{ft}\end{array}$

Conclusion:

The altitude of B when the parachute open is 4296ft

(c)

To determine

To find:The sky driver land first or not.

Answer to Problem 52RE

The B helicopter lands first

Explanation of Solution

Given information:

Skydivers A and B are in a helicopter hovering at 6400 feet. The Skydiver A jumps and descends for 4 see before opening her parachute. The helicopter when climbs to 7000 feet and hovers there. Forty-?ve seconds after A leaves the aircraft. B jumps and descends for 13 sec before opening her parachute. Both skydivers descend at 16 ft/sec with parachutes open.

Formula used:

  $\left(\begin{array}{l}\text{Distance falling by A}\\ \text{before open the parachute}\end{array}\right)=\frac{1}{2}g{t}^2$

Calculation:

Let t represent the number of seconds after A jumps. For $t\ge 4$ sec, A’s position is given by

  $\begin{array}{l}{x}_A\left(t\right)=6144-16\left(t-4\right)\\ x_A\left(t\right)=6288-16t\end{array}$

Since,

At ground

  $\begin{array}{l}{x}_A\left(t\right)=0\\ 6208-16t=0\\ t=388\sec \end{array}$

Now, B’s position is given by for

  $\begin{array}{l}t\ge 45+13\\ t\ge 58\\ x_B\left(t\right)=4296-16\left(t-58\right)\\ x_B\left(t\right)=5224-16t\end{array}$

Since,

At ground

  $\begin{array}{l}{x}_B\left(t\right)=0\\ 5224-16t=0\\ t=326.5\sec \end{array}$

So, B lands first.

Conclusion:

The B helicopter lands first