Math

CalculusCalculus of a Single VariableMoving Shadow A ball is dropped from a height of 20 meters. 12 meters away from the top of a 20-meter lamppost (see figure), The ball's shadow, caused by the light at the top of the lamppost, is moving along the level ground. How fast is the shadow moving 1 second after the ball is released? ( Submitted by Dennis Gittinger, St. Philips College, San Antonio. TX )BuyFind*arrow_forward*

11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275361

Chapter 2.6, Problem 48E

Textbook Problem

**Moving Shadow** A ball is dropped from a height of 20 meters. 12 meters away from the top of a 20-meter lamppost (see figure), The ball's shadow, caused by the light at the top of the lamppost, is moving along the level ground. How fast is the shadow moving 1 second after the ball is released? (*Submitted by Dennis Gittinger, St. Philips College, San Antonio. TX*)

Expert Solution

To determine

**To Calculate:** How fast the shadow moving 1 second after the ball is released.

**Given:**

A ball is dropped from the height of 20 meters, 12 meters away from the top of 20 meter lamppost (in below figure).The ball’s shadow caused by the light at the top of lamppost is moving along the level ground.

**Formula Used:**

Congruency of similar triangle as per AA criteria

Newton's equation of motion

**Calculation:**

Consider the below figure.

By applying the Newton's equation of motion

Here

and

Substituting the values in equation (1), we get

Differentiating with respect to

When time =1 second

Calculus of a Single Variable

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Finding Derivatives In Exercises 99 and 100, the...Ch. 2.4 - Doppler Effect The frequency F of a fire truck...Ch. 2.4 - Harmonic Motion The displacement from equilibrium...Ch. 2.4 - Pendulum A 15-centimeter pendulum moves according...Ch. 2.4 - Wave Motion A buoy oscillates in simple harmonic...Ch. 2.4 - Modeling Data The normal daily maximum...Ch. 2.4 - HOW DO YOU SEE IT? The cost C (in dollars) of...Ch. 2.4 - Biology The number N of bacteria in a culture...Ch. 2.4 - Depreciation The value V of a machine t years...Ch. 2.4 - Finding a Pattern Consider the function f(x)=sinx,...Ch. 2.4 - Conjecture Let f be a differentiable function of...Ch. 2.4 - Think About It Let r(x)=f(g(x)) and s(x)=g(f(x)),...Ch. 2.4 - Using Trigonometric Functions (a) Find the...Ch. 2.4 - Even and Odd Functions (a) Show that the...Ch. 2.4 - Proof Let u be a differentiable function of x. Use...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Linear and Quadratic Approximations The linear and...Ch. 2.4 - Linear and Quadratic Approximations The linear and...Ch. 2.4 - True or False? In Exercises 121-124. determine...Ch. 2.4 - True or False? 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In Exercises 112, find the indicated value: a. xPx2 b. xCx2

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For each of the graphs in 8 and 9: (i) Find all edges that are incidents to v1 . (ii) Find all vertices that ar...

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Refer to the time series in exercise 17. Suppose the values of the time series for the next two time periods ar...

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