Question

8. In the first 10 seconds after its launch, a rocket only moves vertically with an acceleration given by ay(t) (2.40 m/s3)t. * (The asterisks relates to special instruction given only to students in PHY 1999.) a. Calculate the vertical height of the rocket at 10 s. Answer: 400 m. b. Calculate the speed of the rocket when it is 300 meters above the launchpad.

Answer 1

a_y (r) = 2.40 t dv/dt = 2.4 t integral dv = integral 2.4 t middot dt v = 2.4 t^2/2 = 1.2 t^2 ds/dt = 1.2 t^2 integral ds = integral 1.2 t^2 middot dt s = 1.2 t^3/3 = 0.4 t^3 a) At t = 10 sec s = 0.4 times 10^3 = 400 m b) s = 300 m 300 = 0.4 t^3 t = 9.085 sec v = 1.2 t^2 v = 99.05 m/sec