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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640

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BuyFindarrow_forward

Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

FALLING OBJECT Joan is looking straight out a window of an apartment building at a height of 32 ft from the ground. A boy on the ground throws a tennis ball straight up by the side of the building where the window is located. Suppose the height of the ball (measured in feet) from the ground at time t is h(t) = 4 + 64t − 16t2.

  1. a. Show that h(0) = 4 and h(2) = 68.
  2. b. Use the Intermediate Value Theorem to conclude that the ball must cross Joan’s line of sight at least once.
  3. c. At what time(s) does the ball cross Joan's line of sight? Interpret your results.

(a)

To determine

To show: The value for h(0) is 4 and h(2) is 68 for the given function.

Explanation

Given information:

Equation of height h as a function of time t is given as,

h(t)=4+64t16t2 (1)

Where,

  • h is the height of the ball from the ground.
  • t is time.

Calculation:

Substitute 0 for t in equation (1) and get the value of h(0) .

h(0)=4+64×016×

(b)

To determine

To show: The ball crosses Joan’s line of sight at least once using intermediate value theorem.

(c)

To determine

To find: Time(s) at which the ball crosses Joan’s line of sight.

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