Question

A particle a is projected with an initial velocity of 60m/s at an angle 30 degrees to the horizontal.At the same time a second particle b is projected in opposite direction with initial speed of 50m/s from a point at a distance of 100m from
a. If the particles collide in air find the angle of projection of b

Answer 1

Answer:

shown below

Explanation:

first body

x = 60t cos 30 = 30√3t , t = x/30√3

y = 60t sin 30 - gt²/2 = 30t -5t²

y = x/√3 - 5x²/270

y = x/√3 - x²/54

second body

x = 50t cos ∝ + 100  , t = x -100/50cos∝

y = 50t sin ∝ - gt²/2 = (x-100)tan∝ - 5(x-100)²sec²∝

now

(x-100)tan∝ - 5(x-100)²sec²∝ = x/√3 - x²/54

5(x-100)²sec²∝ - x²/54 = (x-100)tan∝ - x/√3