A mountain climber stands at the top of a 50.0 m cliff...

A mountain climber stands at the top of a 50.0 m cliff hanging over a calm pool of water. The climber throws two stones vertically $1.0 \mathrm{s}$ apart and observes that they cause a single splash when they hit the water. The first stone has an initial velocity of $+2.0 \mathrm{m} / \mathrm{s}$ a. How long after release of the first stone will the two stones hit the water? b. What is the initial velocity of the second stone when it is thrown? c. What will the velocity of each stone be at the instant both stones hit the water?

A mountain climber stands at the top of a 50.0 m cliff hanging over a calm pool of water. The climber throws two stones vertically $1.0 \mathrm{s}$ apart and observes that they cause a single splash when they hit the water. The first stone has an initial velocity of $+2.0 \mathrm{m} / \mathrm{s}$
a. How long after release of the first stone will the two stones hit the water?
b. What is the initial velocity of the second stone when it is thrown?
c. What will the velocity of each stone be at the instant both stones hit the water?

Key Concepts

Uniformly Accelerated Motion

This refers to motion where the acceleration is constant, such as free fall under gravity. The common kinematic equations that relate displacement, initial velocity, time, and final velocity are applied, allowing one to predict the motion of objects like the stones as they fall from a height.

Vertical Projectile Motion

This concept describes the motion of an object thrown or dropped along the vertical axis, where gravity is the only acceleration acting on it. It involves analyzing upward and downward movements, determining time-of-flight, and evaluating the impact velocity on reaching a lower height.

Kinematics Equations

The kinematic equations are mathematical formulas that describe the relationships between displacement, time, initial velocity, final velocity, and acceleration. They serve as the foundational tool to solve problems in projectile motion and free fall by providing a systematic method to compute quantities like time to impact and final velocity at landing.

Relative Timing in Sequential Motions

This concept involves analyzing motions that start at different times but interact or coincide at a later event, such as two stones landing at the same moment. The time difference between their releases must be accounted for when applying the kinematic equations, ensuring that their trajectories are correctly synchronized for events such as simultaneous splashes.

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