A landing craft of mass 12000 kg prepare itself for moon landing. when at a vertical distance 160m above the moons surface its downward velocity is 15 m/s. a retrorocket is fired to give the craft an upward thrust to slow its speed to zero as it meet the surface.calculate the needed thrust to decelerate the craft its initial downward velocity to zero as it lands.
This is what i did but i totally could of got it so wrong. this assignment is way harder then i thought it would be :)
Landing craft mass=12000kg
d=160m above moon surface
Vi=15m/s
g on earth=9.81m/s
g on moon g/6
g on moon=1.635m/s
Vf=0m/s
Needed thrust=??
Assuming the crafts mass doesn’t change
Assuming no interference like a moonbuggy in the way.
t=d/s
t=160m/15m/s
t=10.7seconds
a=Vf-Vi/t
a=0m/s-15m/s/10.7
a=-1.40
F=ma
12000x-1.4
=-16800N
To calculate the needed thrust to decelerate the landing craft from its initial downward velocity to zero as it lands, we can use the principle of conservation of energy.
First, let's calculate the gravitational potential energy of the landing craft at a vertical distance of 160m above the moon's surface. The formula for gravitational potential energy is:
PE = mgh
Where:
PE = gravitational potential energy
m = mass of the landing craft
g = acceleration due to gravity (approximately equal to 1.6 m/s^2 on the moon)
h = vertical distance
Substituting the given values, we have:
PE = (12000 kg) * (1.6 m/s^2) * (160 m)
PE = 3072000 J
Next, let's calculate the initial kinetic energy of the landing craft when its downward velocity is 15 m/s. The formula for kinetic energy is:
KE = (1/2)mv²
Where:
KE = kinetic energy
m = mass of the landing craft
v = velocity
Substituting the given values, we have:
KE = (1/2) * (12000 kg) * (15 m/s)²
KE = 1350000 J
Since the craft needs to slow down to zero velocity, the final kinetic energy would be zero. Therefore, the change in kinetic energy is:
ΔKE = 0 - 1350000 J
ΔKE = -1350000 J
According to the principle of conservation of energy, the change in gravitational potential energy is equal to the change in kinetic energy plus the work done by the retrorocket. So, we can write the equation:
ΔPE = ΔKE + work done by retrorocket
Substituting the values we calculated, we can solve for the work done by the retrorocket:
3072000 J = -1350000 J + work done by retrorocket
work done by retrorocket = 3072000 J - (-1350000 J)
work done by retrorocket = 4422000 J
Therefore, the needed thrust to decelerate the landing craft is equal to the work done by the retrorocket. In this case, the work done by the retrorocket is 4422000 Joules.