Answer:
(a) [tex]1.02\times 10^{6}\ kg[/tex]
(b) a = [tex]4.9\ m/s^{2}[/tex]
(c) v' = 2940 m/s
(d) h = 1764 km
Solution:
As per the question:
Weight of the rocket, W = [tex]1\times 10^{7}\ N[/tex]
Lift-off force, F = [tex]1.5\times 10^{7}\ N[/tex]
Now,
To calculate:
(a) Mass of the rocket:
Calculate the mass from the weight of the rocket:
W = mg
where
m = mass of the rocket
Thus
[tex]m = \frac{W}{g} = \frac{1\times 10^{7}}{9.8} = []
(b) To calculate acceleration at lift-off:
F = m(g + a)
[tex]a + g = \frac{1.5\times 10^{7}}{1.02\times 10^{6}}[/tex]
a = 14.7 - g = 14.7 - 9.8 = [tex]4.9\ m/s^{2}[/tex]
(c) To calculate the velocity:
Use kinematic eqn:
v' = u + at
u = initial velocity = 0 m/s
v' = at = [tex]4.9\times 10\times 60 = 2940 m/s[/tex]
(d) To calculate the height, h:
Use kinematic eqn:
[tex]h = \frac{1}{2}gt^{2} = 0.5\times 9.8\times (10\times 60)^{2} = 1764000\ m = 1764\ km[/tex]
