A silver dollar is dropped from the top of a building that is 1326 feet tall. Use the position function below for free-falling objects.

Question

s(t) = −16t² + v₀t + s₀

(a) Determine the position and velocity functions for the coin.

s(t)= -16t^2+1326

v(t)= -32t

(b) Determine the average velocity on the interval [1, 2].

 -48 ft/s

(c) Find the instantaneous velocities when t = 1 second and t = 2 seconds.

v(1) =  -32 ft/s

v(2) =  -64 ft/s

(d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.)

t =  s

(e) Find the velocity of the coin at impact. (Round your answer to three decimal places.)

 ft/s

Answer 1

s(t) = -16t^2 + 1326 = 0 when it hits the ground

16t^2 = 1326

t^2 = 1326/16 = 82.875

t = about 9.104 seconds to reach the ground

v(sqr1326/2) = -32(9.1035) = about 291.314 feet per second velocity when it hits the ground