Chapter 5.8, Problem 78E

(a)

To determine

To graph: The function for the velocity of the object when the air resistance is neglected where an object is thrown upwards at a velocity of 500 feet per second.

(b)

To determine

To calculate: The position function of the object and the maximum height it attains where an object is thrown upwards at a velocity of 500 feet per second.

(c)

To determine

To calculate: The velocity function when air resistance is factored in and the equation is ${\displaystyle \int \frac{dv}{32+k{v}^2}=-{\displaystyle \int dt}}$

(d)

To determine

To graph: The velocity function obtained in part (c) with the value of k as 0.001 and to determine the time at which the maximum height is obtained.

(e)

To determine

To calculate: The approximate value of the integral ${\displaystyle \underset{0}{\overset{t_0}{\int }}v\left(t\right)dt}$ where $t_0$ is the time when the object is at the maximum height.

(f)

To determine

The reason behind the results in parts (b) and (c), the effect of air resistance on the maximum height.