Ch. 03 - Kinematics in Two or Three Dimensions; Vectors

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 03 - Kinematics in Two or Three Dimensions; Vectors

Problem 33

Chapter 3, Problem 33

A diver running 2.5 m/s dives out horizontally from the edge of a vertical cliff and 3.5 s later reaches the water below. How high was the cliff and how far from its base did the diver hit the water?

Verified step by step guidance

Determine the height of the cliff using the vertical motion of the diver. Since the diver starts with no initial vertical velocity, use the kinematic equation for vertical displacement:

y = \frac{1}{2} g t^{2}

, where

g

is the acceleration due to gravity (9.8 m/s²) and

t

is the time (3.5 s).

Substitute the values into the equation:

y = \frac{1}{2} (9.8) ({3.5}^{2})

. This will give the height of the cliff.

Determine how far from the base of the cliff the diver lands by analyzing the horizontal motion. Use the equation for horizontal displacement:

x = v

₀t, where

v

₀ is the initial horizontal velocity (2.5 m/s) and

t

is the time (3.5 s).

Substitute the values into the equation:

x = (2.5) (3.5)

. This will give the horizontal distance traveled by the diver.

Combine the results from the vertical and horizontal motion to fully describe the diver's trajectory. The height of the cliff corresponds to the vertical displacement, and the distance from the base corresponds to the horizontal displacement.

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Key Concepts

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

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is subject to the force of gravity. In this scenario, the diver's horizontal velocity remains constant while the vertical motion is influenced by gravitational acceleration. Understanding the separation of horizontal and vertical components is crucial for analyzing the diver's trajectory.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. For vertical motion, the equation h = 0.5 * g * t^2 can be used to calculate the height of the cliff, where h is the height, g is the acceleration due to gravity (approximately 9.81 m/s²), and t is the time of fall. These equations allow us to relate time, distance, and acceleration.

Horizontal Distance Calculation

The horizontal distance traveled by the diver can be calculated using the formula d = v * t, where d is the distance, v is the horizontal velocity, and t is the time of flight. Since the diver runs at a constant speed of 2.5 m/s for 3.5 seconds, this concept helps determine how far from the base of the cliff the diver lands in the water.

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