Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 14th Edition

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

Young & Freedman Calc 14th Edition

Ch 03: Motion in Two or Three Dimensions

Problem 11

Chapter 3, Problem 11

Crickets Chirpy and Milada jump from the top of a vertical cliff. Chirpy drops downward and reaches the ground in 2.70 s, while Milada jumps horizontally with an initial speed of 95.0 cm/s. How far from the base of the cliff will Milada hit the ground? Ignore air resistance.

Verified step by step guidance

First, understand that Chirpy and Milada are both subject to gravitational acceleration, which is approximately 9.81 m/s² downward. Chirpy drops straight down, while Milada jumps horizontally.

Since Milada jumps horizontally, her initial vertical velocity is 0 m/s. The time it takes for her to hit the ground is the same as Chirpy, which is 2.70 seconds.

Calculate the vertical distance fallen using the formula for free fall:

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

, where

g

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

t

is the time (2.70 s).

Next, calculate the horizontal distance Milada travels using the formula:

x = v t

, where

v

is the horizontal velocity (95.0 cm/s, converted to meters per second) and

t

is the time (2.70 s).

Finally, compute the horizontal distance using the values obtained from the previous steps to find out how far from the base of the cliff Milada will hit the ground.

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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 involves the movement of an object thrown or projected into the air, subject to only the acceleration of gravity. In this scenario, Milada's horizontal jump is a classic example, where her horizontal velocity remains constant while her vertical motion is influenced by gravity, allowing us to calculate her trajectory and landing point.

Free Fall

Free fall describes the motion of an object under the influence of gravitational force alone. Chirpy's drop is a free fall, where the only force acting is gravity, causing him to accelerate downward at 9.8 m/s². This concept helps determine the time it takes for both crickets to reach the ground, which is crucial for calculating Milada's horizontal displacement.

Horizontal Displacement

Horizontal displacement refers to the distance traveled by an object in the horizontal direction. For Milada, this is calculated using her initial horizontal speed and the time she is in the air. Since air resistance is ignored, her horizontal velocity remains constant, allowing us to use the formula: displacement = velocity × time, to find how far she lands from the cliff base.

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