Question

an astronaut jumps from the surface of the moon and follows the path shown by the dashed line. at point p, the astronaut is at the highest point in the path. air resistance is negligible. is the astronaut in equilibrium? why or why not?
a yes, because the astronaut only has a constant horizontal velocity.
b yes, because the astronauts vertical velocity is instantaneously zero.
c no, because the astronaut has a component of velocity in the horizontal direction.
d no, because there is a downward net force on the astronaut.

Explanation:

Step1: Recall the condition for equilibrium

An object is in equilibrium when the net force acting on it is zero (\(\sum F = 0\)).

Step2: Analyze the forces on the astronaut

On the Moon, the astronaut is under the influence of the Moon's gravitational force. At point \(P\), although the vertical component of velocity is zero (but this is not the criterion for equilibrium), there is still a downward gravitational force (\(F = mg_{Moon}\), where \(g_{Moon}\) is the acceleration due to gravity on the Moon) acting on the astronaut. Since there is a non - zero net force (the gravitational force), the astronaut is not in equilibrium.

• Option A: Just having a constant horizontal velocity does not mean the net force is zero. There is still the gravitational force acting, so this option is incorrect.
• Option B: Zero vertical velocity at a point does not imply equilibrium. Equilibrium is about force balance, not velocity, so this option is incorrect.
• Option C: Having a horizontal component of velocity is not related to the equilibrium condition (which is about force), so this option is incorrect.
• Option D: Since there is a downward net force (the Moon's gravity) acting on the astronaut (\(\sum F

eq0\)), the astronaut is not in equilibrium. This option is correct.

Answer:

D. No, because there is a downward net force on the astronaut.