Using the conservation of momentum,
ma*va1 + mb*vb1 = ma*va2 + mb*vb2
Let:
ma = mass of the ball
va = velocity of the ball
mb = mass of the man
vb = velocity of the man
The subscript 1 is known as initials while 2 is for finals.
Before the man throws the ball, he starts at rest, meaning the initial velocity of the ball and the initial velocity of the man are zero. So
0 = ma*va2 + mb*vb2
Given ma = 10 kg; va = 20 m/s; mb = 90 kg; vb is unknown, therefore
-(mb*vb2) = ma*va2
vb2 = -(ma*va2)/mb2 = -(10*20)/90 = -2.22 m/s
Notice that his velocity is negative because when he finally throws the ball (say to the right), he moves at the opposite direction (that is to the left) on which he stands on the frictionless surface.
Answer:
Part a)

Part b)

Explanation:
Part a)
Angular speed of the pedal is changing from 60 rpm to 90 rpm in 10 s
so the angular acceleration is given as

so we will have


now the tangential acceleration of the pedal is given as



Part b)
Total angular displacement made by the sprocket in the interval of 10 s is given as



now length of the chain passing over it is given as



1. Marie and her husband discovered polonium, a new radioactive element, and radium. Marie was the first woman to receive a Novel Prize , and two in her lifetime. She was also the first scientist to receive two Nobel Prizes. Not only that, she was the first person to receive two Nobel Prizes in two different fields, Chemistry and Physics. During World War 1 Marie helped soldiers by creating the x ray. After the war ended Marie raised money to help cure and treat disease using radiology.
2. I am not exactly sure what is happening in that picture but it looks like a boat floating on sea than sunken by a shipwreck on dry land.