Question

2 towers AB and CD are situated a distance d apart. AB is 20m high and CD is 30m high from the ground. An object of mass m is thrown from the top of AB horizontally with a velocity of 10m/s towards CD. Simultaneously another object of mass 2m is thrown from the top of CD at an angle of 60° to the horizontal towards AB with the same magnitude of initial velocity as that of the first abject. The 2 objects move in the same vertical plane, collide in mid air and stick to each other.

i) Calculate the distance d between the towers.

ii) Find the position where the objects hit the ground.

Explain in detail.

Answer 1

Let us assume that the two objects meet after time t.no matter what their masses are both will experience same acclⁿ due to gravity.
let us write down the eqns of motion of particle projected from AB:
x=10t and y=1/2gt²=h
eqns of motion of particle projected from CD:
x=10cos60⁰t and h=10sin60⁰t+1/2gt²
when the two particles strike each other
h_AB+10=h_CD
1/2gt²+10=10sin60⁰t+1/2gt²
on solving 10t=20/(3)^1/2m =distance travelled by particle projected from AB and t=2/(3)^1/2
i.e distance travelled by other particle is=10X1/2X2/(3)^1/2=10/(3)^1/2m
i.e d=10(3)^1/2m.