If a rocket with a mass of 3900 tons vertically accelerates at a rate of # 7/8 m/s^2#, how much power will the rocket have to exert to maintain its acceleration at 5 seconds?

Question

Leo Abeyta · Accepted Answer

Approximately #182.14# megawatts.

We first find the net force acting on the rocket using Newton's second law of motion, which states that, #F_"net"=ma# where: #F_"net"# is the net force in newtons #m# is the mass in kilograms #a# is the acceleration in meters per second squared Here, the net force is the force applied to the rocket by acceleration plus the rocket's weight. #:.F_"net"=ma+mg# #=m(a+g)# Substituting our values, we get: #F_"net"=3900000 \ "kg"(0.875 \ "m/s"^2+9.8 \ "m/s"^2)# #=41632500 \ "N"# Now, we find the velocity of the rocket, given by the equation: #v=u+at# where: #v# is the final velocity #u# is the initial velocity #a# is the acceleration #t# is the time taken Assuming #u=0#, we find the rocket's speed after five seconds: #v=0+0.875 \ "m/s"^2*5 \ "s"# #=4.375 \ "m/s"# Power is given by the equation: #P=F*v# where: #P# is the power in watts #F# is the force in newtons #v# is the velocity in meters per second So, we get: #P=41632500 \ "N"*4.375 \ "m/s"# #=182142188 \ "W"# #~~182.14 \ "MW"#

Elena Albarran · Answer

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

$$
\text{{Power}} = \text{{Force}} \times \text{{Velocity}}
$$

Where Force is equal to mass times acceleration. Given the mass of the rocket and its acceleration, you can calculate the force. Then, you can use the velocity of the rocket at 5 seconds to find the power.