The height of a rocket launched upward from a 160 foot cliff is modeled by the function h(t)= -16t^2+48t+160, where h is height in feet and t is time in seconds. Find the time it takes the rocket to reach the ground at the bottom of the cliff.

Accepted Solution

Answer:5 secondsStep-by-step explanation:In order to find the time when it landed, we will have to find the x-intercepts. Equation given to us : -16t² + 48t + 160 Let's take the GCD, which is -16. -16( t² - 3t - 10 )Factoring what's inside the brackets, we get the x-intercepts. What multiples to -10 but adds up to -3? The numbers are -5 and 2-16 ( t - 5 ) ( t - 2 )X-intercepts are t - 5 and t - 2 Which is 5 and 2 seconds. But one of this is an extraneous solution and that is 2. If we substitute the value of 2 in the equation, we will not get 0. During the x-intercept, the x has a value and y is 0. If we substitute 5 ans x. we will get y as 0. Hence, the answer is 5 seconds.