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?
1 Answer
Approximately
Explanation:
We first find the net force acting on the rocket using Newton's second law of motion, which states that,
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.
Substituting our values, we get:
Now, we find the velocity of the rocket, given by the equation:
where:
#v# is the final velocity
#u# is the initial velocity
#a# is the acceleration
#t# is the time taken
Assuming
Power is given by the equation:
where:
#P# is the power in watts
#F# is the force in newtons
#v# is the velocity in meters per second
So, we get: