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Tanya kicks a ball into the air. The function that models this scenario is f(t) = –16t2 + 96t, where h is the height of the ball in feet and t is the time seconds.
When will the ball hit the ground?
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Given:
The function that models the trajectoy of ball: f(t) = –16t² + 96t.
H is the height of the ball.
t is time in seconds.
To Find:
The time when the ball hits the ground.
Given the trajectory f(t) = -16t² + 96t.
We know
- A projectile follows a parabolic path.
- It will reach its maximum height and fall back.
- Time taken by the ball to reach its maximum height = time taken by the ball to fall to ground from the maximum height.
- Since it follows a parabolic path, it will have maxima at (T,H) , where T is half of time of flight.
Therefore derivative of function at Time Of Flight/2 will be 0.
- df(t)/dt = f'(t) = -32t + 96 = 0
- t = 96/32 = 3 sec.
- Time of flight/2 = 3 sec
- Time of flight = 6 sec.
Time taken by the ball to hit the ground is 6 seconds.
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