BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 38RE
To determine

Tofind:how fast the water skiersrises after she leaves the ramp.

Expert Solution

Answer to Problem 38RE

She rises 7.73ft/s above from the ramp.

Explanation of Solution

Given:

  dhdt=5ft/sec

  dxdt=15ft/sec

Concept used:

Slope of the any object is tanθ or dydx .

If sinθ=k then θ=sin-1k or arcsink .

Calculation:

Let

x=the vertical height of the skier.

H=the distance on the ramp (the hypotenuse) from the beginning of the ramp.

Since, dhdt=30ft/s .

The angle of elevation of the ramp is θ=arctan415 .

An equation that relate the quantities is

  xh=sin(arctan415) .

  x=sin(arctan415)h .

Differentiating with respect to time t

  dxdt=sin(arctan415)dhdt .

Plugging the given data:

  dxdt=sin(arctan415).30

  dxdt=7.73ft/s

Hence, she rises 7.73ft/s above from the ramp.

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