An inquistive student, determined to test the law of gravity for himself, walks to the top of a building og 145 floors, with every floor of height 4 m, having a stopwatch in his hand (the first floor is at a height of 4 m from the ground level). From there he jumps off with negligible speed and hence starts rolling freely. A rocketeer arrives at the scene 5 s later and dives off from the top of the building to save the student. The rocketeer leaves the roof with an initial downward speed `v_0`. In order to catch the student at a sufficiently great height above ground so that the rocketeer and the student slow down and arrive at the ground with zero velocity. The upward acceleration that accomplishes this is provided by rocketeer's jet pack, which he turns on just as he catches the student, before the rocketeer is in free fall. To prevent any discomfort to the student, the magnitude of the acceleration of the rocketeer and the student as they move downward together should not exceed 5 g.
In Q.1, what would be the approximate retardation to be given by jet pack along for safe landing?

Options

A. `5 g ms^(-2)`
B. `2 g ms^(-2)`
C. `4 g ms^(-2)`
D. Cannot be determined

Answer

A

Explanation

a. From solution 2, velocity of rocketeer at the time of catching the boy is
`v = v_0 + gt = 185 ms^(-1)`
For safe landing, final velocity =0
`rArr 0= v^2 - 2 xx a xx s [ s= 400m] rArr agt4g`
So, the acceleration produced by jet pack along would be (4g
`+g) ms^(-2)` in upward direction, as due to gravity, acceleration
g is acting in downward direction.