Question

A boy can throw a stone to a maximum height of $50m$. To what maximum range can he throw this stone and to what height so that the maximum range is maintained?

• A. $100m,100m$
• B. $100m,25m$
• C. $200m,50m$
• D. $100m,50m$

Answer 1

The correct option is B $100m,25m$

For maximum height, the boy has to throw the stone at $\theta ={90}^o$ , then $H=\frac{u^2}{2g}or{u}^2=2gH$
Maximum range $=\frac{u^2}{g}=\frac{2gH}{g}=2H=100m$
Greatest height for maximum range is given by $=\frac{u^2}{2g}{\sin }^2{45}^0=H{\left(\frac{1}{\sqrt{2}}\right)}^2=\frac{H}{2}=25m$