Answer:
The object takes 3.84 seconds to return to earth.
Explanation:
Projectile Motion
It's when an object projected above the ground at a certain velocity, moves along a curved path under the action of gravity.
The initial velocity has two components, given by:
[tex]v_x=vo_x[/tex]
[tex]v_y=vo_y-gt[/tex]
Where vox is the initial component of the velocity in the horizontal direction, voy is the initial component of the velocity in the vertical direction, and t is the time.
The object reaches a maximum height and then it returns to the ground. The time it takes to reach the maximum height can be calculated when the vertical component of the velocity is zero:
[tex]vo_y-gt=0[/tex]
[tex]\displaystyle t_m=\frac{vo_y}{g}[/tex]
The initial vertical component of the velocity is 18.8 m/s, thus:
[tex]\displaystyle t_m=\frac{18.8}{9.8}=1.92~s[/tex]
The total time is double that time:
[tex]t_t=2*1.92~s=3.84~s[/tex]
The object takes 3.84 seconds to return to earth.
