Question

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

Answer 1

(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)