Question

Time of flight (T) = 1s
$\frac{2{\mathrm{u}}_{\mathrm{y}}}{\mathrm{g}}=1\mathrm{s}$                ⇒    u_y = 5 m/s
Range (R) = 4m
     $\frac{2\left({\mathrm{u}}_{\mathrm{x}}\right)\left({\mathrm{u}}_{\mathrm{y}}\right)}{\mathrm{g}}=4$    ⇒    u_x = 4 m/s
$\mathrm{u}=\sqrt{{\mathrm{u}}_{\mathrm{x}}^2+{\mathrm{u}}_{\mathrm{y}}^2}=\sqrt{41}\mathrm{m}/\mathrm{s}$
$\mathrm{\theta }={\tan }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}}{{\mathrm{u}}_{\mathrm{x}}}\right)={\tan }^{-1}\left(\frac{5}{4}\right)$
$\mathrm{H}=\frac{{\mathrm{u}}_{\mathrm{y}}^2}{2\mathrm{g}}=\frac{{\left(5\right)}^2}{20}=\frac{5}{4}=1.25\mathrm{m}$

Time of flight (T) = 1s
$\frac{2{\mathrm{u}}_{\mathrm{y}}}{\mathrm{g}}=1\mathrm{s}$                ⇒    u_y = 5 m/s
Range (R) = 4m
     $\frac{2\left({\mathrm{u}}_{\mathrm{x}}\right)\left({\mathrm{u}}_{\mathrm{y}}\right)}{\mathrm{g}}=4$    ⇒    u_x = 4 m/s
$\mathrm{u}=\sqrt{{\mathrm{u}}_{\mathrm{x}}^2+{\mathrm{u}}_{\mathrm{y}}^2}=\sqrt{41}\mathrm{m}/\mathrm{s}$
$\mathrm{\theta }={\tan }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}}{{\mathrm{u}}_{\mathrm{x}}}\right)={\tan }^{-1}\left(\frac{5}{4}\right)$
$\mathrm{H}=\frac{{\mathrm{u}}_{\mathrm{y}}^2}{2\mathrm{g}}=\frac{{\left(5\right)}^2}{20}=\frac{5}{4}=1.25\mathrm{m}$

Time of flight (T) = 1s
$\frac{2{\mathrm{u}}_{\mathrm{y}}}{\mathrm{g}}=1\mathrm{s}$                ⇒    u_y = 5 m/s
Range (R) = 4m
     $\frac{2\left({\mathrm{u}}_{\mathrm{x}}\right)\left({\mathrm{u}}_{\mathrm{y}}\right)}{\mathrm{g}}=4$    ⇒    u_x = 4 m/s
$\mathrm{u}=\sqrt{{\mathrm{u}}_{\mathrm{x}}^2+{\mathrm{u}}_{\mathrm{y}}^2}=\sqrt{41}\mathrm{m}/\mathrm{s}$
$\mathrm{\theta }={\tan }^{-1}\left(\frac{{\mathrm{u}}_{\mathrm{y}}}{{\mathrm{u}}_{\mathrm{x}}}\right)={\tan }^{-1}\left(\frac{5}{4}\right)$
$\mathrm{H}=\frac{{\mathrm{u}}_{\mathrm{y}}^2}{2\mathrm{g}}=\frac{{\left(5\right)}^2}{20}=\frac{5}{4}=1.25\mathrm{m}$