A small spaceship whose mass is 1.5x10^3 kg (include-ing an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a 10 kW laser beam, what speed will the ship attain in 1.0 day because of the momentum carried away by the beam?

To find the speed attained by the spaceship due to the momentum carried away by the laser beam, we can use the principle of conservation of momentum.

The momentum carried away by the laser beam is equal to the change in momentum of the spaceship. Mathematically, we can write this as:

m * Δv = Δp

where:
m is the mass of the spaceship (including the astronaut)
Δv is the change in velocity/speed of the spaceship
Δp is the change in momentum

The momentum carried by the laser beam can be calculated using the power of the laser beam (P) and the time over which it is exerted (t). Since power is the rate of doing work, and work is the change in energy, we can write:

Δp = P * t

Substituting this into the first equation, we get:

m * Δv = P * t

Now let's substitute the given values:

m = 1.5 * 10^3 kg
P = 10 kW (which is equivalent to 10,000 watts)
t = 1 day = 24 * 60 * 60 seconds

Converting the power to SI units, we have:

P = 10,000 watts

Substituting these values into the equation, we get:

(1.5 * 10^3 kg) * Δv = (10,000 watts) * (24 * 60 * 60 seconds)

Simplifying, we have:

Δv = (10,000 watts) * (24 * 60 * 60 seconds) / (1.5 * 10^3 kg)

Calculating this, we find:

Δv ≈ 1.6 m/s

Therefore, the speed attained by the spaceship due to the momentum carried away by the laser beam is approximately 1.6 m/s.