A body is projected from ground level with initial speed at an angle to the horizontal

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A body is projected from ground level with initial speed

v_0

at an angle

\theta_0

to the horizontal. (a) Obtain an expression for

\dfrac{dy}{dx}

, the slope of the trajectory, in terms of

x

v_0

\theta_0

and

g

. (b) Hence show that the direction of motion of the projectile at any point makes an angle

\phi

with the horizontal given by

\tan\phi = \tan\theta_0 - \dfrac{g x}{v_0^2 \cos^2\theta_0}

. (c) The maximum height reached by the projectile is

H

. Determine the value of

\phi

when the height

y

of the projectile is

\dfrac{H}{2}