# A parachutist is descending at a contant rate of 4.8 ft/s. If someone at a height 15 foot throws an object at an initial velocity of 40 ft/s towards the parachutist when they were 40/6 ft above...

A parachutist is descending at a contant rate of 4.8 ft/s. If someone at a height 15 foot throws an object at an initial velocity of 40 ft/s towards the parachutist when they were 40/6 ft above the ground, the height of the object is given by the function h=-16t^2+40t+15, where t is time in seconds since the item was thrown. The parachutist missed the item, but caught it on its way down. What linear function can be used to find the parachutist's height in terms of t (number of seconds since the item was thrown). Treat the two functions as a system and solve. What does the intersection point mean in context of the problem?

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### 1 Answer

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.**