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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Rolling a Ball Bearing A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is 6. The distance (in meters) the ball bearing rolls in s ( t ) = 4.9 ( sin θ ) t 2 .

(a) Determine the speed of the ball bearing after t seconds.

(b) Complete the table and use it to determine the value of 6that produces the maximum speed at a particular time.

θ 0 π / 4 π / 3 π / 2 2 π / 3 3 π / 4 π
s ' ( t )

(a)

To determine

To calculate: The speed of the ball bearing if s(t)=4.9(sinθ)t2.

Explanation

Given:

The function s(t) gives the distance covered of the ball bearing placed at an angle of elevation θ

s(t)=4.9(sinθ)t2

Formula used:

The speed is the rate of change of the distance with respect to time.

This implies that the function for speed can be computed by differentiating the function for distance with respect to time.

Calculation:

Differentiate the function s(t) with respect to t to obtain:

ddt(s(t))=ddt(4.9(sinθ)t2)=4

(b)

To determine

To calculate: The value of θ at which the speed is maximum at a particular time and to complete the provided table if s(t)=4.9(sinθ)t2.

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