Final answer:
Using the kinematic equation for the displacement of a rock thrown upward, we can calculate the time when the rock will be 10 meters above the water using a quadratic equation. We determine the positive value of time corresponding to the rock's descent to find when it will be 10 meters from the water.
Step-by-step explanation:
In Physics, the motion of the rock thrown upward from a cliff can be analyzed using the equations of motion under the influence of gravity. The question is to find out when the rock will be 10 meters from the water below. Since the rock is thrown from a height of 24 meters, when the rock is 10 meters above the water, it would have fallen 24 - 10 = 14 meters from the starting point at the top of the cliff.
To find the time when the rock is 14 meters below the starting point, we can use the kinematic equation for uniformly accelerated motion:
S = ut + (1/2)at^2
where:
- S is the displacement
- u is the initial velocity (20 meters per second)
- t is the time
- a is the acceleration (due to gravity, which is -9.81 m/s^2, since it's acting downwards)
Substituting the known values, we get:
14 = 20t - (1/2)(9.81)t^2
This is a quadratic equation which can be rewritten as:
(1/2)(9.81)t^2 - 20t + 14 = 0
Using the quadratic formula, we can solve for t:
t = (-b ± √(b^2 - 4ac)) / (2a)
where:
- a = (1/2)(9.81)
- b = -20
- c = 14
The values of t calculated from the quadratic formula represent the times when the rock is both on its upward journey and on its way down. We select the positive value that corresponds to the rock on its way down to answer the question.