Question

Two projectiles are fired from the ground level at equal speeds but different angles at an angle of 30 degree and the other one fired at 60° the projectile to hit the ground first would be the one fired at which degree neglect air resistance

Answer 1

Equation of motion of projectile, launched at an angle $\theta$ with initial speed $v_0$ is $y(t) = v_0 \sin\theta t - \frac{g t^2}{2}$. When it reaches the ground, $y(t) = 0$, from where $t(v_0 \sin \theta -\frac{g t}{2}) = 0$, so it takes $t = \frac{2 v_0 \sin \theta}{g}$ to reach the ground. Since $\sin 30 = 0.5$ and $\sin 60 \approx 0.87$, and $v_0$ is the same for both cases, projectile fired at an angle $30^{\circ}$ will reach the ground faster.