Physics

Problem

Two projectiles P and Q are launched from the same point on level ground with the same initial speed

v

. They return to the point of projection. Their horizontal ranges are equal to

R

but their maximum heights are different, being

H_1

for P and

H_2

(>H_1)

for Q. a. (i) Show that the projection angles

\theta_1

and

\theta_2

satisfy

\displaystyle \tan \theta_i = \dfrac{4H_i}{R}

for

i = 1,2

. b. (ii) Hence obtain explicit expressions for

\theta_1

and

\theta_2

in terms of

H_1

H_2

and

R

. c. (iii) If

R = 80\,\text{m}

H_1 = 10\,\text{m}

and

H_2 = 40\,\text{m}

, calculate

\theta_1

\theta_2

and the common initial speed

v

. Take

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