Force F acts for time duration t.
Acceleration = F / m = a ,
as F is constant , a is constant.
v² - u² = 2 a s = 2 F / m * s
v² - 0 = 2 F s / m
1/2 m v² = F . s
But s = u t + 1/2 a t² = 0 + 1/2 F/m * t²
KE = 1/2 m v² = F * 1/2 F t²/m = F² t² / 2m
K.E. = 1/2 m v^2
As K.E. is proportional to mass and velocities of bodies after falling 30 ft are both same for both masses, the ratio is ratio of masses = 1 : 2.
OR, another way:
K.E. = 1/2 m (u^2 + 2 g h) = m g h,
h = height fallen, g = acceleration due to gravity, m = mass
KE1 / KE2 = m1 g h / m2 g h = m1 / m2 = 1 : 2
a) Work is done against friction force between ground and legs, and it is positive.
b) person studying, if there is no movement, there is no work. This is the picture in the bigger scene at high level.
However, the reading activity involves, movement of eye muscles from left to right or right to left and top to bottom. If more is to be read, there is work done in moving lips, moving neck from left to right.
Hence there is work done by muscles against the friction force faced by muscles.
When we read or see, images form on retina and these are taken to the brain through electrical voltage pulses (of magnitude milli volts). So charge travels distance. There is work done. It is positive.
c) a crane lifting - a bucket of concrete.
The change in potential energy is the work done by the crane on the bucket of concrete. There may not be change in KE of concrete between initial and final states. But the position of concrete has changed in the Earth's gravitational field.
d) work done by the gravitational force on bucket of concrete = - change in the potential energy. This is negative. Gravity pulls an object down. In that case work is done by gravity and is positive. Here the object has increased height. So work is done against gravity and so it is negative work done by gravity.
e) I dont know. perhaps it is supposed to be zero ?
c , d -- my answer is different from that you have given.