Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m with the same velocity of 25 ms^-1. When and where will the two bullets collides? (Take, g = 10 ms^-2)

detailed solution

Correct option is A

Given, distance between the two buildings, d = 100 mHeight of each tower, h = 200 mSpeed of each bullet, v = 25 ms-1The situation can be shown as belowwhere, x be the vertical distance travelled from the top of the building and t be the time at which they collide. As two bullets are fired toward each other, so their relative velocity will bevrel=25-(-25)=50 ms-1Then, time,  t=dvrel=10050=2 sThe distance or height at which they collide is calculated from equation of motion,x=ut+12at2The bullet is initially at rest, i.e., u = 0 and as it is moving under the effect of gravity a = -g, sox=-12gt2x=-12×10(2)2=-20 mThe negative sign shows that the bullets will collide 20 m below the top of tower, i.e. at a height of (200 - 20) = 180 m from the ground after 2 s.