The parachutist is descending at a constant rate of 4.8 ft/s. When the parachutist is at a height of 40/6 ft above the ground an object is thrown from a height of 15 feet towards the parachutist. The height of the object is given by ho = -16t^2 + 40t...
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The parachutist is descending at a constant rate of 4.8 ft/s. When the parachutist is at a height of 40/6 ft above the ground an object is thrown from a height of 15 feet towards the parachutist. The height of the object is given by ho = -16t^2 + 40t + 15 where t is the time after the object is thrown. The function that gives the height of the parachutist a duration of time t after the object is thrown towards him is given by hp = 40/6 - 4.8*t
When the object is caught by the parachutist the height ho and hp should the same.
This gives: -16t^2 + 40t + 15 = 40/6 - 4.8*t
=> -48t^2 + 120t + 45 = 20 - 14.4*t
=> 48t^2 - 134.4*t - 25 = 0
Solving the equation gives the positive root t = `(sqrt(8931)+84)/60`
The time t derived is that at which both the object and the parachutist at the same height.