If a rocket with a mass of 3500 tons vertically accelerates at a rate of # 2/5 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 4 seconds?

Question

Sebastian Acosta · Accepted Answer

2240000 Watts

Firstly, We know, Power = Force x Velocity For the force, we know that F = m x a , where m is the mass and a is the acceleration of the body. In this case, F = 3500 x 1000 x #2/5#, where 1000 is for converting tons to kg. So, F = 1,400,000 Newtons. Now we need to find the velocity at 4 s. We know that a = #2/5# #ms^2#, t = 4s, initial velocity ( u) = 0 #ms^2#, So, a = #(v - u) / t # Therefore, v = 1.6 #ms^2# So, P = 1,400,000 x 1.6 = 2240000 Watts.

Adam Arnold · Answer

undefined To find the power exerted by the rocket, use the formula:

Power = Force * Velocity

First, find the force exerted by the rocket using Newton's second law:

Force = mass * acceleration

Substitute the given values:

Force = 3500 tons * 2/5 m/s^2

Then, find the velocity of the rocket at 4 seconds using the formula:

Velocity = initial velocity + acceleration * time

Substitute the given values:

Velocity = 0 + (2/5 m/s^2) * 4 s

Now, calculate the velocity.

Finally, use the calculated force and velocity to find the power exerted by the rocket.