In: Physics
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.
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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