Question

A particle is projected at an angle of elevation alpha and after t second it appears to have an elevation beta as seen from the point of projection. Find the initial velocity of projection

Answer 1

Answer:

Explanation:

A particle is projected at angle of projection a and after t seconds it appears to have an angle b

with the horizontal. We want to determine the initial velocity.

Let the magnitude of the initial velocity be u.

⇒

The vertical component of the initial velocity is usina and the horizontal component is ucosa.

After t

seconds, the vertical component of velocity becomes usina−gt, where g

is the acceleration due to gravity.

The horizontal component of the velocity remains constant at ucosa.

⇒

The slope of the tangent to the path of the projectile after time t is usina−gtucosa.

The particle is at an angle b

with the horizontal after time t.

⇒

The slope of the tangent to the path of the projectile after time t is tanb.

⇒usina−gtucosa=tanb⇒usina−gt=ucosatanb.