Final answer:
Using the kinematics formula and setting the final velocity to 0 m/s, the time it takes for the rock to reach its highest point with an initial velocity of 22 m/s is approximately 2.24 seconds.
Step-by-step explanation:
To calculate how long it will take for the rock to reach its highest point where the velocity is 22 m/s, we use the kinematics formula that relates initial velocity, acceleration due to gravity, and time. Since the acceleration due to gravity (g) is approximately 9.81 m/s2 (downwards), we can set up the equation for the upward motion:
v = u + at
Where:
- v is the final velocity (0 m/s at the highest point),
- u is the initial velocity (22 m/s upwards),
- a is the acceleration (negative due to gravity, -9.81 m/s2),
- t is the time (which we want to find).
Setting the final velocity (v) to 0 m/s since the rock will momentarily stop at its highest point:
0 = 22 + (-9.81)t
t = 22 / 9.81
t ≈ 2.24 seconds
Therefore, it takes approximately 2.24 seconds for the rock to reach its highest point.