SOLUTION: The height of a football t seconds after a punt depends upon the intital height & velocity of the ball and on the downward pull of gravity. Suppose a punt leaves the kicker's foot
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Question 183894: The height of a football t seconds after a punt depends upon the intital height & velocity of the ball and on the downward pull of gravity. Suppose a punt leaves the kicker's foot at an initial height of 0.8 meters with initial upward velocity of 20 meters per second.
A. Write an algerbraic rule relating flight time t in seconds and height h in meters for this punt.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The acceleration due to Earth gravity is approximately 9.8 meters per second.
(Note: the constant is negative because it is in the opposite direction to the upward initial velocity vector)
The instantaneous velocity is given by the integral of acceleration with respect to time where the constant of integration is the initial velocity.
 = \int g\,dt = gt + v_o = -9.8t + v_o\text{ m/sec})
The instantaneous height is given by the integral of the velocity fuction (V(t)) respect to time where the constant of integration is the initial height.
 = \int V(t) = \int gt + v_o = -\frac{1}{2}gt^2 + v_ot + h_o = -4.9t^2 + v_ot + h_o \text{ m})
For your situation:
 = -4.9t^2 + 20t + 0.8\text{ m})
John
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