A toy rocket fired straight up into the air has heights(t)= 160t-16t2 feer after t seconds.
(a) what is the rocket's initial velocity (when t = 0)??
(b) what is the velocity after 2 seconds?
(c) what is the acceleration when t=3?
(d) at what time will the rocket hit the ground?
(e) at what velocity will the rocket be traveling just as it smashes into the ground
(a) at t=0 whats vilocity (in other words,find v(0) )
s(t)=160t-16t2
s'(t) = v(t) =160-32t
v(0) = 160-32(0) = 160 ft/s
(b) find v(2).
v(2) = 160-32(2) = 96 ft/s
(c) find a(3)
a(t) = v'(t) = -32 ft/s^2
a(3) = -32 ft/s^2
(d) find when the position will be equal to zero (ie, that's when it hits the ground is s=0)
s(t) = 0 = 160t-16t2
t = 0 or t=10 (we use t = 10 becasue at t=0, its beinglauched and at t=10, its comming back)
(e) find v(10)
v(10) = 160-32(10) = -160ft/s (minus sign indicates thatvilocity is in down y-direction)
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