Final answer:
To find the time for the rock to reach its maximum height, we use the kinematic equation with the initial velocity of 29.9 m/s and the acceleration as -9.81 m/s^2 resulting in an approximate time of 3.05 seconds.
Step-by-step explanation:
The time it will take for the rock to reach its maximum height can be calculated by using the kinematic equations of motion for uniformly accelerated motion. Assuming the only acceleration is due to gravity (g = 9.81 m/s2), which acts downwards, the initial velocity (v0) upwards is 29.9 m/s opposite to gravity.
The equation to use is v = v0 + at, where v is the final velocity (0 m/s at the maximum height), v0 is the initial velocity, a is the acceleration due to gravity (which will be -9.81 m/s2 because it's in the opposite direction of the throw), and t is the time. Solving for t gives t = (v - v0)/a.
Plugging the values into the equation: t = (0 - 29.9 m/s) / (-9.81 m/s2) which simplifies to t = 29.9 m/s / 9.81 m/s2. Thus, the time taken to reach maximum height is approximately 3.05 seconds.