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 are expelled at a speed of 1750 m/s, how much mass must be expelled.

deltamass*velocity gas= 3180*vperp

So figure the new vperp of the rocket to give a 35degree change with initial velocity 114 (tan35=Vperp/115 ?)
then figure deltamass

This is not correct.

To find the amount of mass that must be expelled by the rocket, we can use the principle of conservation of momentum.

Let's assume the mass of the expelled gases is m kg.

The initial momentum of the rocket is given by:
Initial momentum = (mass of the rocket) * (velocity of the rocket)

The final momentum of the rocket after firing the rockets perpendicularly is given by:
Final momentum = (mass of the rocket - m) * (final velocity of the rocket) + m * (velocity of the expelled gases)

According to the conservation of momentum, the initial momentum and final momentum must be equal. Therefore, we can write the equation as:

(mass of the rocket) * (velocity of the rocket) = (mass of the rocket - m) * (final velocity of the rocket) + m * (velocity of the expelled gases)

Now, let's substitute the given values into the equation:

(3180 kg) * (115 m/s) = (3180 kg - m) * (115 m/s) + m * (1750 m/s)

Expanding the equation, we have:

365700 kg·m/s = (365700 kg - 115m) m·s + 1750m^2·kg/s

Now, let's further simplify the equation:

365700 kg·m/s = 365700 kg·m/s - 115m m·s + 1750m^2·kg/s

By canceling out the common units, we have:

0 = -115m + 1750m^2

Now, let's solve this quadratic equation:

1750m^2 - 115m = 0

Factorizing the equation:

m(1750m - 115) = 0

Setting each factor equal to zero:

m = 0 or 1750m - 115 = 0

The first solution, m = 0, does not make physical sense because it implies that no mass is expelled from the rocket.

Solving the second equation for m:

1750m - 115 = 0
1750m = 115
m = 115 / 1750
m ≈ 0.0657 kg

Therefore, approximately 0.0657 kg of mass must be expelled from the rocket to alter its course by 35.0 degrees.

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the rockets are fired is equal to the total momentum after the rockets are fired.

The total momentum before firing the rockets can be calculated as the product of the rocket's total mass and its velocity:

Total momentum before = Total mass × Velocity

Total momentum before = 3180 kg × 115 m/s

To change the rocket's course, we need to calculate the change in momentum. Since the rockets are fired in a direction perpendicular to the original motion, the change in momentum can be found using the formula:

Change in momentum = Mass of expelled gases × Exhaust velocity

This change in momentum is equal to the momentum of the rocket after the rockets are fired, which can be calculated by:

Total momentum after = Mass of rocket × Final velocity

Since the rocket changes its course by 35.0 degrees, we need to break the velocity vector into its components: one parallel to the original motion and one perpendicular to it. The parallel component will remain unchanged, while the perpendicular component will change to zero.

The final velocity of the rocket can be calculated using trigonometry:

Final velocity = Initial velocity × sin(35.0 degrees)

Substituting this into the equation for the total momentum after firing the rockets gives:

Mass of rocket × (Initial velocity × sin(35.0 degrees)) = Mass of expelled gases × Exhaust velocity

Now we can solve for the mass of expelled gases:

Mass of expelled gases = (Mass of rocket × (Initial velocity × sin(35.0 degrees))) / Exhaust velocity

Mass of expelled gases = (3180 kg × (115 m/s × sin(35.0 degrees))) / 1750 m/s

Evaluating this expression will give us the mass of expelled gases needed to alter the course of the rocket.