Question

A particle is projected at an angle of projection alpha and after t second it appears to have an angle of beta with horizontal . The initial velocity is​

Answer 1

Answer:

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.  

⇒u(sina−cosatanb)=gt⇒u=gtsina−cosatanb.

⇒ The magnitude of the initial velocity is gtsina−cosatanb.

Explanation:

Answer 2

Answer:

equating horizontal components and solving...