Question

A football kicker can give the ball an initial speed of 25.0 m/s. What are the (a) least and (b) greatest elevation angles at which he can kick the ball to score a field goal from a point 50.0 m in front of goalposts whose horizontal bar is 3.44 m above the ground? When doing this, you may want to research some trig identities to get a formula involving only tangent functions. Also, since there are two values of angle that will work, maybe the quadratic formula is involved.

Answer 1

Given:

Initial launch velocity,

Condition to score a field goal: When the horizontal distance covered by the football is 50m, the vertical height of the football must be 3.44m.

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Consider the horizontal motion of the football

There is no acceleration in the horizontal direction, so horizontal velocity remains constant.

Horizontal speed = Horizontal Distance/Time

-------(1)

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Consider the vertical motion of the football

Use formula

Initially, the football is going up and g is acting downwards, so put a negative sign for g.

Put (1) in the above equation

Note:

Let

Solve the quadratic equation using a calculator

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Case 1:

ANSWER:

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Case 2:

ANSWER:

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