Respuesta :
If a rock is dropped from a height of 178 ft, its position is given by the function s(t) = -16t² + 178.
a. It takes 3.34 s to reach for the rock to hit the ground.
b. The average velocity of the rock from when it is released until it hits the ground is 53.3 ft/s.
c. At 1.66 s, its instantaneous velocity will be equal to average velocity.
a. The given function is s(t) = -16t² + 178
To find t, we have to equate the distance to zero.
0 = -16t² + 178
16t² = 178
t² = 11.125
t = 3.34 s
b. The rock is said to be dropped from a height of 178 ft. Its average velocity is calculated by dividing the displacement of the rock upon total time taken to reach the ground.
v = 178/ 3.34 = 53.3 ft/s
c. The instantaneous velocity is calculated by differentiating s(t) with respect to t. And then equate it with the average velocity of the rock.
-32 t = 53.3
t = 1.66 s
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