Motion in a Plane

Step 1: Write the formula for rangeThe formula to find the range $R$ when a body is projected is:$R = \frac{u^2 \sin 2\theta}{g}$Step 2: Put in the given valuesHere, $R = 180\sqrt{3}\ \mathrm{m},\ u = 60\ \mathrm{m/s}$, and $g = 10\ \mathrm{m/s^2}$.Step 3: Arrange the formula to find $\sin 2\theta$$\sin 2\theta = \frac{R g}{u^2}$Step 4: Substitute the values$\sin 2\theta = \frac{180\sqrt{3} \times 10}{60 \times 60}$$\sin 2\theta = \frac{1800\sqrt{3}}{3600} = \frac{\sqrt{3}}{2}$Step 5: Identify the angle for $\sin 2\theta$We know that $\sin 60^{\circ} = \frac{\sqrt{3}}{2}$.So, $2\theta = 60^{\circ}$$\theta = 30^{\circ}$Step 6: Check for other possible anglesThe range at angle $\theta$ is the same as at $90^{\circ} - \theta$.So, the angle of projection can be $30^{\circ}$ or $60^{\circ}$.