Question

From the ground level, a ball is to be shot with a certain speed. Graph shows the range $R$ it will have versus the launch angle $\theta$. The least speed the ball will have during its flight, if $\theta$ is chosen such that the flight time is half of its maximum possible value, is equal to (take g = 10 $m/s^2$):

• A. $250m/s$
• B. $50\sqrt{3}$
• C. $50m/s$
• D. $25\sqrt{3}$

Answer 1

The correct option is D $25\sqrt{3}$

Time of flight is given by:
$T=\frac{2usin\theta }{g}$
maximum possible value is:
$T_{max}=\frac{2u}{g}$
Half of the maximum time of flight is obtained at $\theta ={30}^{\circ }$
because, $sin{30}^o=0.5$
Range is given by:
$R=\frac{u^{2}sin2\theta }{g}$
Max value is $R_{max}=\frac{u^2}{g}=250m$
Solving that we get $u=50m{s}^{-1}$
Minimum velocity in flight $=u\times cos\theta =50\times cos{30}^{\circ }=25\sqrt{3}m{s}^{-1}$