(Q.6) A toy rocket fired straight up into the air has height ​s(t) = 160t − 16t^2 feet after t seconds.

Question

(a) What is the​ rocket's initial velocity​ (when t =​ 0)? _________ (Answer).

(b) What is the velocity after 4 seconds? _________ (Answer).

(c) What is the acceleration when t = 8​? ___________ (Answer).

(d) At what time will the rocket hit the​ ground? _______ (Answer).

(e) At what velocity will the rocket be traveling just as it smashes into the​ ground? ________ (Answer).

Answer 1

s(t) = 160t - 16t^2

s'(t) = v(t) = 160 - 32t = velocity

a(t) = s''(t) = v'(t) = -32 = acceleration (deceleration)

a) v(0) = 160-32(0) = 160 feet per second

b) v(4) = 160-16(4)^2 = 160 - 16(16) = 160- 256 = -96 feet per second negative 96 means it's going down at

96 feet per second

c) a(8) = -32 feet per second per second = -32 ft/sec^2, just the force of gravity

d) 0=160t-16t^2 = t(160-16t) 16t=160, t = 10 seconds to the hit the ground

e) v(10) = 160-32(10) - 160-320 = - 160 feet per second velocity