Superman and the Hulk are playing baseball. The Hulk throws a fast ball to Superman and it is hit straight up in the air. Hulk is standing 60.5 feet from Superman when the ball is hit. Assuming the ball never comes back down ( rememberSuperman just hit it), write a model that represents the angle of elevation (from Hulk's perspective) as a function of the height of the ball.

[tex]The \ angle \ of \ elevation, \ \theta,\ as \ a \ function \ of \ height, \ h \ is \ \underline{ \theta = tan^{-1}\left( \dfrac{h}{60.5} \right)}[/tex]

What type of function can be used to model the angle of elevation of the ball?

The given parameters are;

The distance the Hulk throws the fastball to Superman = 60.5 feet

The direction Superman hits the ball = Straight up

Required:

The angle of elevation of the ball from the Hulk's perspective.

Solution:

Let, h, represent the height of the ball, and let, θ, represent the angle of

elevation of the ball, from trigonometric ratios, we have;

[tex]tan(\theta) = \mathbf{\dfrac{Opposite \ side \ to \ angle \ \theta }{Adjacent \ side \ to \ angle \ \theta}}[/tex]

The side opposite to the angle θ from the Hulk's perspective is the

height, h, of the ball = h

The adjacent side = Distance between Hulk and Superman = 60.5 feet

Therefore;

[tex]tan(\theta) = \mathbf{ \dfrac{h}{60.5}}[/tex]

Which gives;

[tex]The \ angle \ of \ elevation, \ \underline{ \theta = tan^{-1}\left( \dfrac{h}{60.5} \right)}[/tex]

Learn more about trigonometric ratios here:

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