Two blocks of ice, one four times as heavy as theother, are at rest on a frozen lake. a person pushes each block thesame distance d. ignore friction and assume that an equal force f_vec is exerted on each block.
this is what i have sofar:
parta
which of the following statements istrue about the kinetic energy of the heavier block after thepush?
it is equalto the kinetic energy of the lighter block.
partb
compared to the speed of the heavierblock, how fast does the light block travel?
twice asfast
this is what i cant figure out:
partc
now assume that both blocks have thesame speed after being pushed with the same force f_vec. what can be said about the distances the two blocks arepushed?
a the heavyblock must be pushed 16 times farther than the lightblock.
b the heavyblock must be pushed 4 times farther than the lightblock.
c the heavyblock must be pushed 2 times farther than the lightblock.
d the heavytblock must be pushed the same distance as the lightblock.
e the heavyblock must be pushed half as far as the light block.

A.

B. the lighter block travels at a speed 4 times faster than the heavier block.

C. b The heavy block must be pushed 4 times farther than the light block.

Explanation:

Given that the blocks are  acted upon by equal force.

A.

Then the kinetic energy of the blocks depends on their individual velocity.

And velocity is related to momentum through Newton's second law of motion:

considering that the time for which the force acts on each mass is equal.

For the heavier block:

Therefore:

Kinetic energy of lighter block:

Kinetic energy of heavier block:

B.

From the above calculations and assumptions we observe that the lighter block travels at a speed 4 times faster than the heavier block.

C.

Since the lighter block is having the speed 4 times more than the heavier block so it must be pushed 4 times farther because the speed is directly proportional to the  distance.

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be