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?

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Answer 1 · 2018-07-08T13:34:21

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"#