Question

Three astronauts guide a 100 kg asteroid safely away from their space capsule. The first astronaut pushes with a 35 N force directed 45 degrees below the x-axis. The second astronaut pushes with a 35 N force directed 45 degrees above the -axis. The third astronaut pushes with a 35 N force along the x-axis. Calculate the magnitude of the net force exerted by the three astronauts. Calculate the rate (magnitude only) at which the asteroid's velocity changes.

Answer 1

The magnitude of the net force exerted by the three astronauts is 84.5 N and the rate at which the asteroid's velocity changes is 0.845 m/s².

The given parameters;

• mass of the asteroid = 100 kg
• force by first astronaut = 35 N, at 45 degrees below x -axis
• force by second astronaut = 35 N, at 45 degrees above x-axis
• force by third  astronaut = 35 N, at 0 degrees on x-axis

The resultant horizontal force applied by the three astronauts on the asteroid is calculated as;

Fₓ = 35cos(45) + 35cos(45) + 35cos(0)

Fₓ = 84.5 N

The rate at which the asteroid's velocity changes is calculated as;

$F = ma = m\frac{\Delta v}{\Delta t} \\\\\frac{\Delta v}{\Delta t} = \frac{F}{m} \\\\\frac{\Delta v}{\Delta t} = \frac{84.5}{100} \\\\\frac{\Delta v}{\Delta t} = 0.845 \ m/s^2$

Thus, the magnitude of the net force exerted by the three astronauts is 84.5 N and the rate at which the asteroid's velocity changes is 0.845 m/s².

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