Question

(a) Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by

(b) Show that the projection angle for a projectile launched from the origin is given by

Where the symbols have their usual meaning.

Answer 1

(a) Let and respectively be the initial components of the velocity of the projectile along horizontal (x) and vertical (y) directions.

Let and respectively be the horizontal and vertical components of velocity at a point P.

Time taken by the projectile to reach point P = t

Applying the first equation of motion along the vertical and horizontal directions, we get:

(b) Maximum vertical height,

Horizontal range,

Solving equations (i) and (ii), we get: