At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation: $s = 320 t - 16 t ^ { 2 }$
In how many seconds does the object reach its maximum height?
A) 800 sec
B) 1,600 sec
C) 10 sec
D) 5 sec

Question

Quizplus · Accepted Answer

To find the time at which the object reaches its maximum height, we need to find the vertex of the parabolic function given. The vertex has the form (t,s) where t is the time and s is the height reached.

The vertex occurs when the derivative of the function is zero:

s' = 320 - 32t = 0
t = 10

Therefore, the maximum height is reached at t=10 seconds, which is choice D.

At a Time T Seconds After an Object Is Tossed s=320t−16t2s = 320 t - 16 t ^ { 2 }s=320t−16t2

At a Time T Seconds After an Object Is Tossed $s = 320 t - 16 t ^ { 2 }$