Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.

The rock will strike the water with a speed of $24.8 m / s$ and is independent of the direction thrown.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Conservation of energy

Conservation of energy: An isolated system's total energy is always conserved. In other words, the energy neither be created nor be destroyed; it can be only transformed from one form to another.

Mathematically,

$Δ KE = Δ PE \frac{1}{2} m v_{f}^{2} - \frac{1}{2} m v_{i}^{2} = m g h_{f} - m g h_{i}$ (1.1)

Here, m is the mass of the rock, $v_{f}$ is the final velocity of the rock ( $v_{f} = 0$ as the rock stops after striking the water), $v_{i}$ is the initial velocity of the rock, g is the acceleration due to gravity $(g = 9.8 m / s^{2})$ , $h_{f}$ is the final height ( $h_{f} = 0$ as the rock strikes the water), and $h_{i}$ is the initial height or the height of the bridge $(h_{i} = 20.0 m)$ .

Proof that the rock will strike the water with a speed of when thrown downward

Rearranging equation (1.1) to get an expression for the final velocity,

$v_{f} = \sqrt{v_{i}^{2} + 2 g (h_{i} - h_{f})}$ (1.1)

When the rock is thrown downward with initial velocity will be positive i.e., $v_{i} = 15.0 m / s$ . The final velocity can be calculated using equation (1.2).

Putting all known values in equation (1.2),

$v_{f} = \sqrt{{(15.0 m / s)}^{2} + 2 \times (9.8 m / s^{2}) \times [(20.0 m) - (0 m)]} = 24.8 m / s$

Therefore, the rock will strike the water with a speed of $24.8 m / s$ when thrown downward.

Proof that the rock is independent of the direction thrown

When the rock is thrown downward with initial velocity will be negative i.e. $v_{i} = - 15.0 m / s$ . The final velocity can be calculated using equation (1.2).

Putting all known values in equation (1.2),

$v_{f} = \sqrt{{(- 15.0 m / s)}^{2} + 2 \times (9.8 m / s^{2}) \times [(20.0 m) - (0 m)]} = 24.8 m / s$

Therefore, the rock will strike the water with a speed of $24.8 m / s$ when thrown downward.

From the above discussion it is clear that the rock will strike the water with a speed of $24.8 m / s$ and is independent of the direction thrown.

Find Study Materials for

Create Study Materials

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.

Step by Step Solution

Conservation of energy

Proof that the rock will strike the water with a speed of when thrown downward

Proof that the rock is independent of the direction thrown

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

College Physics (Urone)

Answers without the blur.

Short Answer

Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.

Step by Step Solution

Conservation of energy

Proof that the rock will strike the water with a speed of when thrown downward

Proof that the rock is independent of the direction thrown

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics