Question

Skydiving A skydiver is equipped with a stopwatch and an altimeter. As shown in Figure 3.2.7, he opens his parachuteseconds after exiting a plane flying at an altitude offeet and observes that his altitude isfeet. Assume that air resistance is proportional to the square of the instantaneous velocity, his initial velocity on leaving the plane is zero, and.

(a) Find the distance, measured from the plane, the skydiver has travelled during freefall in time.

[Hint: The constant of proportionalityin the model given in Problem 15 is not specified. Use the expression for terminal velocityobtained in part (b) of Problem 15 to eliminatefrom the IVP. Then eventually solve for.

(b) How far does the skydiver fall and what is his velocity at ?

Short answer

Answer:

The distance measured from the plane isand

Step-by-step solution

Define velocity 

It is the pace at which an object's position changes in relation to a frame of reference and time. It may sound difficult, but velocity simply refers to the rate at which something moves in a given direction. It is a vector quantity, which implies that to define velocity, we require both magnitude (speed) and direction.

A variable separable differential equation can be solved using the following ways

Determination of velocity as a function of time

Determination of velocity as a function of time upon further substitution of values

We have,

Substituting the value of, we get

Applying the condition, we get

Using the variable separable method and calculating distance as a function of time

Now applying the conditionseconds), we get

Apply the point of condition to get the distance function

Applyingseconds), we get

Substituting the value of, we get

Substitute  to get the required distance

The velocity afteris

The velocity at the skydiver's fall