## a) To find the mass of the rocket, we can use the equation w = mg, where w is the weight of the rocket and g is the acceleration due to gravity. In this case, the weight of the rocket on the surface of the Earth is given as 1 x 10^7 N. Since the acceleration due to gravity on Earth is approximately 9.8 m/s^2, we can calculate the mass (m) of the rocket by dividing the weight (w) by the acceleration due to gravity (g):

m = w / g

m = 1 x 10^7 N / 9.8 m/s^2

b) To find the acceleration at lift-off, we can use the equation F = ma, where F is the force exerted and a is the acceleration. In this case, the lift-off force is given as 1.5 x 10^7 N. Using the mass (m) from part a, we can calculate the acceleration (a):

a = F / m

a = 1.5 x 10^7 N / (1 x 10^7 N / 9.8 m/s^2)

c) To calculate the speed at which the rocket will be moving after 10 minutes, we can use the equation vf = at, where vf is the final velocity, a is the acceleration, and t is the time. Convert 10 minutes to seconds by multiplying by 60:

t = 10 minutes * 60 seconds/minute

t = 600 seconds

vf = a * t

d) To find the height the rocket will reach after 10 minutes, we can use the equation h = 1/2 * a * t^2, where h is the height, a is the acceleration, and t is the time. We already have the time in seconds:

h = 1/2 * a * t^2