Answer:
a)
& 
b) 
c) 
Explanation:
Given:
mass of the book, 
combined mass of the student and the skateboard, 
initial velocity of the book, 
angle of projection of the book from the horizontal, 
a)
velocity of the student before throwing the book:
Since the student is initially at rest and no net force acts on the student so it remains in rest according to the Newton's first law of motion.

where:
initial velocity of the student
velocity of the student after throwing the book:
Since the student applies a force on the book while throwing it and the student standing on the skate will an elastic collision like situation on throwing the book.

where:
final velcotiy of the student after throwing the book
b)



c)
Since there is no movement of the student in the vertical direction, so the total momentum transfer to the earth will be equal to the momentum of the book in vertical direction.



Answer:
They both rises to same height.
Explanation:
When an object is sliding up in friction less surface than according to conservation of energy its potential energy will be converted into kinetic energy.

Here, m is the mass, v is the velocity, g is the acceleration due to gravity and H is the height.
Here the height is independent on the mass of an object and its only depend on velocity.
Now according to the question, two objects have same velocity but they have different masses.
Therefore, they rises to the same height because height will not change with mass.
If they both are moving with the same speed and direction
i.e. covering the same distance in the same time interval in the same direction