The final velocity (
) of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut (
) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts <em>after throwing the ball</em>.
The given parameters;
- Mass of the first astronaut, = m₁
- Mass of the second astronaut, = m₂
- Initial velocity of the first astronaut, = v₁
- Initial velocity of the second astronaut, = v₂ > v₁
- Mass of the ball, = m
- Speed of the ball, = u
- Final velocity of the first astronaut, =

- Final velocity of the second astronaut, =

The final velocity of the first astronaut relative to the second astronaut after throwing the ball is determined by applying the principle of conservation of linear momentum.

if v₂ > v₁, then
, to conserve the linear momentum.
Thus, the final velocity (
) of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut (
) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts after throwing the ball.
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Answer:

Explanation:
The equivalent of Newton's second law for rotational motions is:

where
is the net torque applied to the object
I is the moment of inertia
is the angular acceleration
In this problem we have:
(net torque, with a negative sign since it is a friction torque, so it acts in the opposite direction as the motion)
is the moment of inertia
Solving for
, we find the angular acceleration:

Answer:
towards the south
Explanation:
When the electron enters the region with magnetic field, it experiences a magnetic force perpendicular to both the directions of the electron's velocity and the magnetic field.
The direction of the force exerted on the electron can be found by using the right-hand rule:
- Index finger: direction of the velocity of the electron --> towards the east
- Middle finger: direction of the magnetic field --> downward
- Thumb: direction of the force on a positive particle --> towards the north
However, the electron is a negatively charged particle, so we must reverse the direction of the force: therefore, the force exerted on the electron is towards the south.