The horizontal range of a projectile fired at an angle of $15°$ is $50m$. If it is fired with the same speed at an angle of $45°$, its range will be

The correct option is C

$100m$

Projectile Motion:

Projectile motion is the motion of an object or particle (a projectile) that is projected near the Earth's surface and moves along a curved path only under the influence of gravity.

Step 1: Given;

Horizontal range of a projectile, $R=50m$

The angle of projection, $\theta =15°$ and then projected at an angle ${\theta }_1=45°$

Step 2: Formula used;

Horizontal range, $R=\frac{u^2\sin 2\theta }{g}$

Step 3: Find the speed when projected at an angle $\theta =15°$;

$$\begin{gathered} 50=\frac{u^2\sin 30}{10} \\ \Rightarrow u^2=1000 \end{gathered}$$

Step 4: Find the range when projected at an angle ${\theta }_1=45°$;

$$\begin{gathered} R=\frac{1000\times 1}{10}(\because u^2=1000;g=10;\sin 90°=1) \\ \Rightarrow R=100m \end{gathered}$$

Hence, the range when projected at an angle ${\theta }_1=45°$ is $100m$.

Thus, option C is the correct answer.