A What is the rockets initial upward acceleration BAt an alt

A) What is the rocket\'s initial upward acceleration?

B)At an altitude of 5000 m the rocket\'s acceleration has increased to 6.4 m/s2 . What mass of fuel has it burned?

Solution

The rocket, at the time of launch, will have two forces acting on it. One due to the rocket\'s thrust and other due to gravitational pull.

That is the net force would be = 2.9 x 10^5 - Mg

a.) Therefore the net acceleration at the time of launch would be:2.9 x 10^5/1.9 x 10^4 - 9.81 = 5.4532 m/s^2

b.) At an altitude of 5000 m, the value of g will decrease slightly. Plus, the weight of the rocket will decrease as well.

The gravitational acceleration at height h is given as g(1 - 2h/R)= 9.81(1 - 10/6400) = 9.79 m/s^2

Now, the net force would be Thrust - Mg\' = Ma

Or 6.4 = 2.9x10^5 / M - 9.79

or, 16.19 = 2.9 x 10^5 /M

or M = 1.79123 x 10^4

Therefore the mass of fuel burnt = Mi - 1.79123 x 10^4 = 1.0877 x 10^3 Kg

NOTE: Here I have taken into consideration the change in gravitational acceleration. However, it needs to be noted that such a change can also be neglected. Hence the answer may differ slighly in that case.