Problema Solution
Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t)= -16t(squared)+16t+480 , where t is the time in seconds and h is the height in feet.
A. How long did it take for Jason to reach his maximum height?
B. What was the highest point that Jason reached?
C. Jason hit the water after how many seconds?
Answer provided by our tutors
Ans A.
h=-16(t^2)+16t+480
dh/dt=-32t+16=0 (;for maximum height)
so t=0.5s
Ans B.
now put t=0.5s into eqn. of h.
so h=-16(0.25)+16(0.5)+480=484 meters.
Ans C.
finding time for hitting the water,Jason has to travell h height with the acceleration of Earth(g).
so h=(1/2)g(t^2)
so 484=(1/2)(9.8)(t^2)
so t=9.93 seconds.