# physics

posted by .

A rocket consists of a payload of 4280.0 kg and 1.626 105 · of fuel. Assume that the rocket starts from rest in outer space, accelerates to its final velocity, and then begins its trip. What is the speed at which the propellant must be expelled to make the trip from the Earth to the Moon, a distance of 3.82 · 105 km, in 9.5 h?

• physics -

Excuse the change in units. 60 year old habits are hard to break.

You left us without a clue as to the weight of the rocket. Propellant fractions of rockets typically range from .85 to .90, i.e., the weight of propellant divided by the fully loaded rocket stage. For this exercise, I will assume .90.

The calculations ignore the energy lost from earth's gravity and the energy gain from the lunar gravity.

The distance to be covered within the 9.5 hr time period is 382,000 km = 237,375 miles. The burnout velocity is therefore 237,375(5280)/9.5(3600) = 36,650 fps.

The rocket is already in an orbit as implied by the problem statement. Assuming the rocket is in a 100 mile high orbit, it already has a circular velocity of 25,618 fps. Therefore, the rocket must only contribute an additional 11,029 fps of velocity. (The escape velocity from this orbit is 36,229 fps.

The delta velocity, dV, derived from the rocket is given by dV = cln(Wo/Wbo where dV = the change in rocket velocity, c = the velocity of the exhaust gases, Wo = the ignition weight and Wbo = the burnout weight.

The rocket weight is 358,533/.9 kg = 398,370 lb. including propellants.

With the 4280 kg payload, the total ignition weight becomes 398,370 + 9437 = 407,807 lb.

The burnout weight is Wbo = 49,274 lb.

The dV contributed by the rocket is dV = cln(407,807/49,274) = 2.1134 making c = 11,029/2,1134 = 5439 fps

These numbers imply a straight line path to the moon, ignoring the more realistic parabolic shape of an escape trajectory.

If you uncover any inconsistencies, feel free to let me know.

## Similar Questions

1. ### physics

Model rocket engines are sized by thrust, thrust duration, and total impulse, among other characteristics. A size C5 model rocket engine has an average thrust of 5.26 N, a fuel mass of 12.7 g, and an initial mass of 25.5 g. The duration …
2. ### physics

i need help figuring out what formaula to use for finding the final velocity of a rocket. Model rocket engines are sized by thrust, thrust duration, and total impulse, among other characteristics. A size C5 model rocket engine has …
3. ### Physics

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +42 ft/s2. After some time t1, the rocket engine is shut down and the sled moves with constant velocity v for a time t2. Assume the total …
4. ### physic

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 …
5. ### Classical Mechanics Physics

Consider a rocket in space that ejects burned fuel at a speed of vex= 1.5 km/s with respect to the rocket. The rocket burns 6 % of its mass in 310 s (assume the burn rate is constant). (a) What is the speed v of the rocket after a …
6. ### Physics

Consider a rocket in space that ejects burned fuel at a speed of vex= 2.0 km/s with respect to the rocket. The rocket burns 8 % of its mass in 300 s (assume the burn rate is constant). (a) What is the speed v of the rocket after a …
7. ### PHYSICS IMP PLS

Consider a rocket in space that ejects burned fuel at a speed of v_ex= 2.0 km/s with respect to the rocket. The rocket burns 10 % of its mass in 290 s (assume the burn rate is constant). (a) What is the speed of the rocket after a …
8. ### PHYSICS(elena)

Consider a rocket in space that ejects burned fuel at a speed of vex= 1.5 km/s with respect to the rocket. The rocket burns 8 % of its mass in 280 s (assume the burn rate is constant). (a) What is the speed v of the rocket after a …
9. ### physics (Urgent)!!!!!!!!!!!!!!!!!!!!!!

Consider a rocket in space that ejects burned fuel at a speed of vex= 1.5 km/s with respect to the rocket. The rocket burns 8 % of its mass in 280 s (assume the burn rate is constant). (a) What is the speed v of the rocket after a …
10. ### physics Classical Mechanics

Consider a rocket in space that ejects burned fuel at a speed of vex= 1.5 km/s with respect to the rocket. The rocket burns 8 % of its mass in 280 s (assume the burn rate is constant). (a) What is the speed v of the rocket after a …

More Similar Questions