Final answer:
The question pertains to the physics of a rock thrown vertically upward with an initial velocity of 24.5 m/s. High school-level kinematics and conservation of energy are applied to calculate the rock's motion and its velocity as it strikes the water after being thrown from a height.
Step-by-step explanation:
The question relates to the motion of a rock thrown vertically upward with an initial velocity. This is a topic usually covered in high school physics classes under mechanics, specifically under the sub-topic of kinematics and energy conservation. In this case, energy considerations will be used to determine the speed with which the rock strikes the water when thrown from a height, as well as to calculate the position and velocity of the rock at different time intervals after being thrown upward from the cliff.
Motion of a Rock Thrown Vertically Upward
When a rock is thrown vertically upward, its motion is governed by the acceleration due to gravity, which is constant and directed downward. Given an initial velocity, we can calculate various parameters of the rock's motion, such as the maximum height reached, the time it takes to reach that height, and the velocity at different points during its motion.
For example, let's consider a rock thrown upward with an initial velocity of 24.5 m/s. Using the equation of motion v = u + at (where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time), the rock will reach its maximum height when its velocity becomes zero. Neglecting air resistance and using the acceleration due to gravity (g = -9.80 m/s²), we can find the time taken to reach the maximum height. We can also use energy conservation principles to find the velocity of the rock at different heights during its ascent and descent.
A similar calculation can be used to show that a rock thrown from a bridge 20 m above water with an initial speed of 15.0 m/s will strike the water with a speed of 24.8 m/s, regardless of the direction in which it was thrown. This is because in the absence of air resistance, the only force acting on the rock is gravity, making its motion only dependent on its initial speed and the height from which it was thrown.