Question

A rocket of total mass 3180 kg is traveling in outer space with a velocity of 115 m/s toward the sun. it wishes to alter its course by 30.0°, and can do this by firing its rockets briefly in a direction perpendicular to its original motion. if the rocket gases are expelled at a speed of 1750 m/s, how much mass must be expelled?

Answer 1

The mass expelled will be 116.239 kg

Step-by-step explanation:

We have given the mass of the rocket M = 3180 kg

Initial velocity of the rocket v= 115 m /sec

Now change in velocity
`v'=vtan30=115* tan30^(\circ)=115* 0.577=66.395m/sec`

From the conservation of momentum change in momentum is equal to the momentum of gas expelled

Let the mass expelled is m

We have also given that speed of the gas expelled
`v_g=1750m/sec`

So
`(M-m)v'=mv_g`

`(3180-m)* 66.395=m* 1750`

`m=116.239kg`

So the mass expelled will be 116.239 kg

Answer 2

Let Vx = 115m/s

in order for the angle to be 30 degrees

tan 30 = Vy/115

Vy = 66.40 m/s

Using conservation of momentum:

m(1750) = (3180 - m) 66.40

1750m = 211152 – 66.40m

1750 m + 664.40 = 211152

1816.40 m = 211152

m = 211152 / 1816.40

m = 116.25 kg would be the answer