# physics

A rocket is fired in deep space, where gravity is negligible. In the first second it ejects 1/160 of its mass as exhaust gas and has an acceleration of 15.1 m/s^2.What is the speed v_gas of the exhaust gas relative to the rocket?

1. 👍 0
2. 👎 0
3. 👁 3,514
1. A rocket is fired in deep space, where gravity is negligible. In the first second it ejects 1/160 of its mass as exhaust gas and has an acceleration of 15.1 m/s^2.What is the speed v_gas of the exhaust gas relative to the rocket?

By means of the rocket equation,

deltaV = cln(Wo/Wt) where
deltaV or dV = the incremental change in velocity over a given time period, Wo = the initial weight at ignition, Wt = the weight after a specific time period and c = the velocity of the exhaust gases. ln = the natural logarithm of.

After one second of firing, the rocket achieves a speed of 15.m/s.

Therefore,
dV = 15.1 = cln[Wo/(Wo-Wo/160)
...= ]5.1 = cln[1/(1-1/160] = ............cln(1.006289)

15.1 = cln(1.006289) - c(.0062696

Hence, c = 2408m/s

1. 👍 2
2. 👎 3

## Similar Questions

1. ### physics

A small weather rocket weighs 14.7 N. The rocket is carried up by a balloon. The rocket is released from the balloon and fired, and its engine exerts an upward force of 10.2 N on the rocket. What is the acceleration of the rocket?

2. ### physics

A 15.0-kg test rocket is fired vertically from Cape Canaveral. Its fuel gives it a kinetic energy of 1961 J by the time the rocket motor burns all the fuel. What additional height will the rocket rise? m - how do you organize

3. ### physics

A test rocket is fired straight up from rest. The net acceleration is 20 m/s2 upward and continues for 4.0 seconds, at which time the rocket engines cease firing. What maximum elevation does the rocket reach?

4. ### Physics

A rocket that weighs 7840 N on earth is fired. The force of propulsion is + 10 440N. Determine a) the mass of the rocket, b) the acceleration of the rocket, c) the velocity of the rocket at the end of 8.0 s.

1. ### Alg/Trig

If h= -16t^2 + 112t represents the height of a​ rocket, in​ feet, t seconds after it was​ fired, when will the rocket hit the​ ground? (Hint: The rocket is on the ground when h equals=​0).

2. ### Calculus

A rocket fired straight in the air is being tracked by a radar station 3 miles from the launching pad. If the rocket is travelling at 2 miles per second, how fast is the distance between the rocket and the tracking station

3. ### physic

A sounding rocket, launched vertically upward with an initial speed of 79.0 m/s, accelerates away from the launch pad at 5.70 m/s2. The rocket exhausts its fuel, and its engine shuts down at an altitude of 1.15 km, after which it

4. ### physics - linear momentum with rockets

A rocket of total mass 3180 kg is traveling in outer space with a velocity of 115 m/s. To alter its course by 35.0 degrees, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases

1. ### math

A rocket is fired into the air with an initial velocity of 98 m/s. The height ( h ) of the rocket after t seconds is given by the expression h = 98t - 4.9t2. a. What the average rate of change over the first 2 seconds. b. At what

2. ### 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

3. ### Physics

A bullet is dropped into a river from a very high bridge. At the same time, another bullet is fired from a gun straight down towards the water. If air resistance is negligible, the acceleration of the bullets just before they

4. ### physics

A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 60.0º above the horizontal. The rocket is fired toward an 15.0 m high wall, which is located 27.0 m away. The rocket attains its launch speed in a