Question

Two particles are projected simultaneously with the same speed u m/s in the same vertical plane with angle 30 and 60 degree with horizontal. At what time their velocities will become parallel

Answer 1

We first write the velocities in vector form.

For a particle projected with some velocity u at an angle Ф to the horizontal, velocity is given by :

U = u Cos Фi + (u sinФ - gt) j

The slope is equal to m and it is equal to :

m = (u Sin Ф - gt) /u Cos Ф

The velocities are parallel when the slopes are equal :

Therefore

(u Sin 30° - gt) / u Cos 30° = (u Sin 60° - gt) / u Cos 60°

When we break this we get :

gt (√3 — 1) = u

t = u /g(√3 — 1)

Answer 2

Answer:

Explanation:

We first write the velocities in vector form.

For a particle projected with some velocity u at an angle Ф to the horizontal, velocity is given by :

U = u Cos Фi + (u sinФ - gt) j

The slope is equal to m and it is equal to :

m = (u Sin Ф - gt) /u Cos Ф

The velocities are parallel when the slopes are equal :

Therefore

(u Sin 30° - gt) / u Cos 30° = (u Sin 60° - gt) / u Cos 60°

When we break this we get :

gt (√3 — 1) = u

t = u /g(√3 — 1)