Answer:
B) 20N.s is the correct answer
Explanation:
The formula for the impulse is given as:
Impulse = change in momentum
Impulse = mass × change in speed
Impulse = m × ΔV
Given:
initial speed = 40m/s
Final speed = -60 m/s (Since the the ball will now move in the opposite direction after hitting the bat, the speed is negative)
mass = 0.20 kg
Thus, we have
Impulse = 0.20 × (40m/s - (-60)m/s)
Impulse = 0.20 × 100 = 20 kg-m/s or 20 N.s
Since Astronaut and wrench system is isolated in the space and there is no external force on it
So here momentum of the system will remain conserved
so here we can say

initially both are at rest
so here plug in all values


so here the astronaut will move in opposite direction and its speed will be equal to 0.20 m/s
Answer:
D
Explanation:
D) The overall work done by gravity is zero
This statement is correct .
If m be the mass of each of the children and h be the height of tower
work done by gravity on the boys in going up = - mgh
it is so because force applied by gravity = mg downwards and displacement
is upwards
work done will be negative = - mgh
Work done by gravity on boys when they come down = + mgh because both force and displacement are downwards .
Hence total work done = - mgh + mgh = 0.
The children will have same kinetic energy as the inclined surface is friction-less so no energy will be dissipated hence addition of energy to boys in both the cases will be same.
Answer:

Explanation:
We know that the tangent function relates the angle of the right triangle that forms the hot air balloon rising:

Differentiating (1) with respect to time, we get:

since x is a constant value. Replacing:
