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Leokris [45]
3 years ago
9

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s2 for 35 s , then ru

ns out of fuel. Ignore any air resistance effects.
a. What is the rocket's maximum altitude?
b. How long is the rocket in the air?
c. Draw a velocity-versus-time graph for the rocket from liftoff until it hits the ground.

Physics
1 answer:
Gre4nikov [31]3 years ago
4 0

Answer:

a) h_m=74625\ m

b) t=265.55\ s

Explanation:

Given:

  • mass of rocket, m_r=200\ kg
  • mass of fuel, m_f=100\ kg
  • acceleration of the rocket consuming fuel, a=30\ m.s^{-2}
  • time after which the fuel exhaust, t_f=35\ s

<u>During the phase of fuel exhaustion:</u>

<u>velocity attained by the rocket just as the fuel ends:</u>

v_f=u+a.t_f

where:

u= initial velocity of the rocket = 0

v_f=0+30\times 35

v_f=1050\ m.s^{-1} this will be the initial velocity for the phase of ascending of the rocket's height under the influence of gravity.

<u>height at which the fuel finishes:</u>

v_f^2=u^2+2a.h_f

1050^2=0^2+2\times 30\times h_f

h_f=18375\ m

<u>During the phase of ascend in height of rocket after the fuel is over:</u>

<u>Time taken to reach the top height after the fuel is over:</u>

v=v_f+g.t'

at top v = (final velocity during this course of motion )= 0 m.s^{-1}

0=1050-9.8\times t'

t'=107.1429\ s

<u>Height ascended by the rocket after the fuel is over:</u>

v^2=v_f^2+2g.h'

at the top height the velocity is zero

0^2=1050^2-2\times 9.8\times h' (-ve sign denotes that the direction of motion is opposite to that of acceleration)

h'=56250\ m

<u>Therefore the maximum altitude attained by the rocket:</u>

h_m=h_f+h'

h_m=18375+56250

h_m=74625\ m

b)

time taken by the rocket to fall back to the earth:

h_m=v.t_m+\frac{1}{2} g.t_m^2

where:

v= initial velocity of the rocket during the course of free fall from the top height.

74625=0+4.9\times t_m^2

t_m=123.41\ s

Now the total time for which the rocket is in the air:

t=t_f+t'+t_m

t=35+107.1429+123.41

t=265.55\ s

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