Question

A projectile is fired with the a speed u at an angle $\theta$ above the horizontal field. The coefficient of restitution be tween the projectile and filed is e. Find the position from the starting point when the projectile will land at its second collision .

• A. $\frac{e^2{u}^{2}sin2\theta }{g}$
• B. $\frac{(1+e^2)u^{2}sin2\theta }{g}$
• C. $\frac{(1+e^2)u^{2}sin\theta cos\theta }{g}$
• D. $\frac{(1+e)u^{2}sin2\theta }{g}$

Answer 1

The correct option is D $\frac{(1+e)u^{2}sin2\theta }{g}$

Vertical velocity after first collision $=eusin\theta$

New Time of flight $T^{\prime }=\frac{2eusin\theta }{g}$,

$R^{\prime }=u_x{T}^{\prime }$

$x=R+R^{\prime }=\frac{u^{2}sin2\theta }{g}(1+e)$