Question

A golfer hits a golf ball with an initial velocity of 100 miles per hour. The range R of the ball as a function of the angle θ to the horizontal is given by R(θ)=672sin(2θ), where R is measured in feet. Round to two decimal places. Write DNE if the solution does not exist.

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​A) At what angle θ should the ball be hit if the golfer wants the ball to travel 450 feet (150 yards)?
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degrees
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B) At what angle θ should the ball be hit if the golfer wants the ball to travel 540 feet (180 yards)?
degrees
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" role="presentation">C) At what angle θ should the ball be hit if the golfer wants the ball to travel at least 480 feet (160 yards)?

degrees

D) At what angle ​ θ should the ball be hit if the golfer wants the ball to travel 720 feet (240 yards)?
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Answer 1

A) 21.02°

B) 26.74°

C) 22.79°

D) DNE

Explanation:

We can solve the equation for the angle:

D = 672·sin(2θ)

D/672 = sin(2θ)

arcsin(D/672) = 2θ

θ = arcsin(D/672)/2

A) For D = 450, θ = arcsin(450/672)/2 = 21.0198° ≈ 21.02°

B) For D = 540, θ = arcsin(540/672)/2 = 26.7363° ≈ 26.74°

C) For D = 480, θ = arcsin(480/672)/2 = 22.7923° ≈ 22.79°

D) For D = 720, θ = arcsin(720/672)/2 = DNE