Answer:
Approximately 3.03 seconds.
Explanation:
The distance traveled in the vertical direction is given by the kinematic equation:
[tex]\displaystyle y = v_{iy}t + \frac{1}{2}at^2[/tex]
Where v_iy and a are the initial velocity and acceleration of the object, respectively, in the vertical direction.
Because the rock is thrown horizontally, there is no horizontal velocity. Therefore:
[tex]\displaystyle y = \frac{1}{2} at^2[/tex]
The vertical acceleration is simply gravity g. This, this yields the general equation:
[tex]\displaystyle y = \frac{1}{2}gt^2[/tex]
Substitute 45 m for y and solve for time t:
[tex]\displaystyle \begin{aligned} (45\text{ m}) & = \frac{1}{2}(9.8\text{ m/s$^2$})t^2 \\ \\ t^2 & =\frac{450}{49}\text{ s$^2$} \\ \\ & \approx 3.03\text{ s}\end{aligned}[/tex]
Therefore, it will take approximately 3.03 seconds for the rock to fall 45 meters vertically.
