A ball is projected from level ground with an initial speed at an angle above the…

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A ball is projected from level ground with an initial speed

v_0

at an angle

\theta

above the horizontal. Neglect air resistance. (a) Write the expressions for the horizontal and vertical displacements of the ball as functions of time

t

. Clearly identify the variables involved. (b) Eliminating

t

, obtain an expression for the horizontal range

R

of the projectile in terms of

v_0

\theta

and

g

. (c) Show that

R

attains its maximum value when the angle of projection satisfies

\theta = 45^\circ

. (d) Hence obtain a formula for the maximum horizontal range

R_{\text{max}}

and calculate its value when

v_0 = 20\,\text{m s}^{-1}

and

g = 9.8\,\text{m s}^{-2}

. Give your answer to two significant figures.

Related theory

Projectile Motion
Motion in a Plane

Browse the problem library