A soccer ball, at rest on the ground, is kicked with an initial velocity of $10\ \mathrm{\displaystyle \frac{m}{s}}$ at a launch angle of $30^\circ $. Calculate its total flight time, assuming that air resistance is negligible.
A) $0.5\ \mathrm{s}$
B) $1\ \mathrm{s}$
C) $2\ \mathrm{s}$
D) $4\ \mathrm{s}$
A) $0.5\ \mathrm{s}$
B) $1\ \mathrm{s}$
C) $2\ \mathrm{s}$
D) $4\ \mathrm{s}$
First, determine the time required for the ball to reach the top of its parabolic trajectory (which is the time required for the vertical velocity to drop to zero).
$$v_y\overset{\mathrm{set}}{=}0$$
$$v_{0y}-gt=0$$
$$t=\frac{v_{0y}}{g}$$
The total flight time is equal to twice this value:
$$t_t=2t$$
$$t_t=2\frac{v_{0y}}{g}$$
$$t_t=2\frac{v_0\sin{\theta_0}}{g}$$
$$t_t=\frac{2\left(10\ \mathrm{\displaystyle \frac{m}{s}}\right)\sin{30^\circ }}{10 \mathrm{\displaystyle \frac{m}{\ s^2}}}$$
$$t_t=1\ \mathrm{s}$$