Writing a Quadratic Model
Cliff Diving
When a driver jumps from a ledge. the vertical component of his motion can be modeled by the vertical motion model. Suppose the ledge is 48 feet above the ocean and the initial upward velocity is 8 feet per second, how long will it take the diver enters the water?
Solution
Use a vertical motion model.
Let and .
Vertical motion model
Substitute values.
To find the time when the diver enters the water, let and solve the resulting equation for t.
Write quadratic model.
Factor out -8.
Factor.
The solutions are and . Negative values for time do not make sense, so the only reasonable solution is . It will take the diver 2 seconds.