You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, 6.006.00 s after it was thrown. What is the speed of the rock just before it reaches the water 28.028.0 m below the point where the rock left your hand? Ignore air resistance.

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

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Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problem 49

Chapter 2, Problem 49

You throw a small rock straight up from the edge of a highway bridge that crosses a river. The rock passes you on its way down, $6.00$ s after it was thrown. What is the speed of the rock just before it reaches the water $28.0$ m below the point where the rock left your hand? Ignore air resistance.

Verified step by step guidance

Identify the known values: the time taken for the rock to pass you on its way down is 6.00 s, and the distance from the bridge to the water is 28.0 m. We need to find the speed of the rock just before it reaches the water.

Use the kinematic equation for vertical motion:

v_{f} = v_{i} + g t

, where

v_{f}

is the final velocity,

v_{i}

is the initial velocity,

g

is the acceleration due to gravity (approximately 9.81 m/s²), and

t

is the time.

Since the rock passes you on its way down after 6.00 s, the initial velocity

v_{i}

can be found using the equation

y = v_{i} t + \frac{1}{2} g t^{2}

, where

y

is the displacement (28.0 m).

Rearrange the equation to solve for

v_{i}

v_{i} = \frac{y - \frac{1}{2} g t^{2}}{t}

. Substitute the known values to find

v_{i}

Finally, substitute the initial velocity

v_{i}

and the time

t

into the kinematic equation to find the final velocity

v_{f}

just before the rock reaches the water.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinematics Equations

Kinematics equations describe the motion of objects under constant acceleration. In this scenario, the rock's motion can be analyzed using these equations to determine its velocity and position at different times. The key equations include those for displacement, velocity, and acceleration, which help calculate the rock's speed just before it hits the water.

Gravitational Acceleration

Gravitational acceleration is the constant acceleration experienced by objects due to Earth's gravity, approximately 9.81 m/s². This concept is crucial for calculating the rock's motion as it travels upwards and then downwards. Understanding gravitational acceleration allows us to determine how the rock's velocity changes over time.

Initial Velocity

Initial velocity is the speed at which an object begins its motion. In this problem, the rock is thrown upwards, and its initial velocity affects its subsequent motion. Knowing the initial velocity helps in applying kinematics equations to find the rock's speed at different points, including just before it reaches the water.

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