To determine how high the rock will go before it starts to fall, we can use the kinematic equations of motion.
Given: Initial velocity (u) = 30 m/s
When the rock reaches its maximum height, its final velocity (v) will be zero because it momentarily comes to a stop before starting to fall. The acceleration due to gravity (g) acts in the opposite direction to the initial velocity.
Using the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
Since the rock comes to rest at the highest point, the final velocity (v) is zero.
0 = (30 m/s)^2 + 2(-9.8 m/s^2)s
Simplifying the equation:
0 = 900 m^2/s^2 - 19.6 m/s^2 s
Rearranging the equation to solve for displacement (s):
19.6 m/s^2 s = 900 m^2/s^2
s = 900 m^2/s^2 / 19.6 m/s^2
s ≈ 45.92 m
Therefore, the rock will reach a height of approximately 45.92 meters before it starts to fall.