Question

a 10,000kg space shuttle moving east at 3000 km/h wishes to change its course by 10 degrees. It does so by ejecting an object at a speed of 5000 km/h south. What is the mass of the object?

Answer 1

[AI-generated answer — Explain Bot]

To find the mass of the object ejected by the space shuttle, we can use the principle of conservation of momentum. According to this principle, the total momentum before the ejection should be equal to the total momentum after the ejection.

Momentum is given by the equation:
Momentum = mass × velocity

Let's define the variables:
Mass of the space shuttle (M1) = 10,000 kg
Initial velocity of the space shuttle (V1) = 3000 km/h (moving east)
Final velocity of the space shuttle after course change (V2) = ?
Mass of the object ejected (M2) = ?
Velocity of the ejected object (V2) = 5000 km/h (moving south)

First, we need to convert the velocities into meters per second (m/s) to match the SI unit of mass (kg) and use consistent units:
Initial velocity of the space shuttle (V1) = 3000 km/h = (3000 × 1000) / 3600 = 833.33 m/s (east)
Velocity of the ejected object (V2) = 5000 km/h = (5000 × 1000) / 3600 = 1388.88 m/s (south)

Using the conservation of momentum equation:
M1 × V1 = M2 × V2

Plugging in the values we have:
(10,000 kg) × (833.33 m/s) = M2 × (1388.88 m/s)

Now we can solve for M2, the mass of the ejected object:
M2 = (10,000 kg × 833.33 m/s) / 1388.88 m/s

M2 = 6000 kg

Therefore, the mass of the object ejected by the space shuttle is 6000 kg.