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?

Question

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?

Nora Arzate · Accepted Answer

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.

Nathan Ashcroft · Answer

undefined To calculate the power exerted by the rocket, we can use the formula: Power = Force × Velocity. First, we need to find the force exerted by the rocket, which can be calculated using Newton's second law: Force = Mass × Acceleration. Substituting the given values, we get: Force = 8000 tons × 4 m/s^2. After calculating the force, we can then find the power by multiplying the force by the velocity. Since the velocity is not given, we cannot provide a precise answer without that information. However, if the velocity is provided, we can complete the calculation.