Question

A parachutist's speed during a free fall reaches 65 meters per second. What is this speed in feet per second? At this speed, how many feetwill the parachutist fall during 20 seconds of free fall? In your computations, assume that I meter is equal to 3.3 feet. Do not round youranswers.

Answer 1

The speed of a parachutitst in free fall is 65m/s. In order to find this velocity in feet per second you use the following identities:

1 m = 100 cm

2.54 cm = 1 in

12 in = 1 ft

Each of the previous identity is used as a convertion factor. You proceed as follow:

where you put as the denominator the quantity with the unit that it is necessay to cancel out. For instance, in the first factor (65m/s) you have meters in the numerator, in order to cancel meter, the next factor (100cm/1m) has to have a denominator with units in meter. Then you have a numerator with centimeters, and you use a factor that allows you to cancel centimeter, as the factor 1in/2.54cm makes.

To calculate the height traveled by the parachutist you use the following formula:

`h=vt+(1)/(2)gt^2`

v: speed of the parachutist = 213.2 ft/s

t: time = 20 s

g: gravitational acceleration = 32ft/s²

You replace the previous values into the formula for h, the height traveled:

`\begin{gathered} h=(213.2(ft)/(s))(20s)+(1)/(2)(32(ft)/(s^2))(20)^2 \\ h=10664ft \end{gathered}`

Hence, the parachutist falls 10664 ft