Answer to Question #140459 in Physics for Nani

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.