Comprehension # 9
In James bond movie ''The Spy Who Loved Me'', James skied down a snowy slope in an attempt to escape from the killer. Unfortunately, the killer had a higher skiing speed than James's, they are `40m//s` and `40m//s` respectively. Now consider an alternative version of the movie.
James noted that he and the killer carried the same kind of rifle' and estimated that their masses M (including body mass, skis, weapon, backpack, ect) were about the same. Recalling high school physics knowledge, James realised that each time he fired his weapon back at the killer, his momentum would change, whereas when the killer fired, the killer's momentum would also change. Evergy time James fired a bullet, the killer would fire back accordingly. Assume that all bullets missed their targets (otherwise this exercise would terminte). Given `M = 100 kg`, mass and the muzzle velocity of a bullet are `m = 0.02 kg` and `v = 500 m//s` respectively

How many bullets James had to fire in order to assure that the killer couldn't catch up with him ?

Options

A. 15
B. 25
C. 45
D. 55

Answer

B

Explanation

Increase in velocity of James for each bullet fired `m_(b)Deltav_(b) = m_(j)Deltav_(J)`
`0.02 xx (500 - 40) = 100 Deltav_(J) " " [v_(b) = v_(bm) v_(J)]`
`Deltav_(J) = (92)/(1000)` (down the plane)
decreases in velocity of killing for each bullet fired `m_(b) v_(b) = m_(K) Deltav_(k)`
`0.02 xx 545 = deltav_(k) xx 100`
`Deltav_(k) = (109)/(1000)` (up the plane)
So decrease in relative velocity for each bullet fired.
`Deltav_(rel) = (92)/(1000) + (109)/(1000) = 0.2 m//s`
So to decrease relative velocity to zero.
No. of bullet fired `n = (1)/(0.5) xx 5 = 25`