If a rocket with a mass of #8000 " tons" # vertically accelerates at a rate of # 4 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 3 seconds?

1 Answer
May 7, 2018

Power is defined as the rate of doing work. As such Power #P# is given as

#P=vecFcdot vecv#

To maintain acceleration of rocket at a rate of #a=4\ ms^-2#, rocket must over come force of gravity acting downwards. As such using Newton's Second Law of motion we get

#F_uarr=m(a+g)#

Inserting given values we get

#F_uarr=8000xx1000(4+9.81)=1.1048xx10^8\ N#

Assuming rocket starts from rest and acceleration is constant, velocity after #3\ s# is found using kinematic expression

#u=u+at#
#v_uarr=0+4xx3=12\ ms^-1#

We see that #cos theta# in the cross product becomes #=1# as force and velocity are in the same direction.

#:.P=(1.1048xx10^8)xx12=1.32xx10^9\ W#, rounded to two decimal places.