Consider a rocket in space that ejects burned fuel at a speed of 1.5 km/s with respect to the rocket. The rocket burns 9 % of its mass in 310 s (assume the burn rate is constant).
(a) What is the speed of the rocket after a burn time of 155.0 s? (suppose that the rocket starts at rest; and enter your answer in m/s)
unanswered
(b) What is the instantaneous acceleration of the rocket at time 155.0 s after the start of the engines?(in m/s )
p: percentage (4.5% is burned in 155s)
m:mass of rocket
u:fuelspeed in meter/s!
v=u*ln(1/(1-p))=1500*ln(1/0.955)
a=v/t
Its incorrect
no it is correct
in numbers 256.5 and 1.71 respectively?
To answer part (a) of the question, we can use the concept of conservation of momentum. We know that the burned fuel is ejected from the rocket at a speed of 1.5 km/s with respect to the rocket.
Let's assume the initial mass of the rocket is M kg. After burning 9% of its mass in 310 s, the remaining mass of the rocket is (1 - 0.09)M = 0.91M kg.
Using the conservation of momentum, we can write:
Initial momentum of the rocket = Final momentum of the rocket
Initial momentum of the rocket = 0 (since initially, the rocket is at rest)
Final momentum of the rocket = (0.91M kg)(V) + (0.09M kg)(-1.5 km/s), where V is the speed of the rocket after the burn time.
Setting up the conservation of momentum equation, we have:
0 = (0.91M kg)(V) + (0.09M kg)(-1.5 km/s)
Simplifying the equation, we get:
0 = 0.91M V - 0.135M
Rearranging the equation to solve for V, we have:
0.135M = 0.91M V
V = 0.135M / 0.91M
V = 0.1484 m/s
Therefore, the speed of the rocket after a burn time of 155.0 s is approximately 0.1484 m/s.
To answer part (b) of the question, we need to calculate the instantaneous acceleration of the rocket at time 155.0 s.
Acceleration is the rate of change of velocity. Since we know the speed of the rocket after 155.0 s from part (a), we can find the acceleration by dividing the change in velocity by the change in time.
Since the rocket starts from rest (zero velocity), the change in velocity is equal to the final velocity (from part (a)).
Acceleration = (change in velocity) / (change in time)
Acceleration = (0.1484 m/s - 0 m/s) / (155.0 s - 0 s)
Acceleration = 0.1484 m/s / 155.0 s
Acceleration ≈ 0.000956 m/s²
Therefore, the instantaneous acceleration of the rocket at time 155.0 s after the start of the engines is approximately 0.000956 m/s².