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Ch 03: Motion in Two or Three Dimensions
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 03: Motion in Two or Three DimensionsProblem 18c
Chapter 3, Problem 18c

A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.0° above the horizontal. The shot hits the ground 2.08 s later. Ignore air resistance. How far did she throw the shot horizontally?

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Identify the initial velocity components. The initial velocity is given as 12.0 m/s at an angle of 51.0° above the horizontal. Use trigonometry to find the horizontal and vertical components: \( v_{x} = v \cdot \cos(\theta) \) and \( v_{y} = v \cdot \sin(\theta) \), where \( v = 12.0 \) m/s and \( \theta = 51.0° \).
Calculate the horizontal component of the velocity. Substitute the values into the equation \( v_{x} = 12.0 \cdot \cos(51.0°) \) to find the horizontal velocity component.
Understand that the horizontal motion is uniform because air resistance is ignored. The horizontal distance traveled, or range, can be calculated using the formula \( d = v_{x} \cdot t \), where \( t = 2.08 \) s is the time of flight.
Substitute the horizontal velocity component and the time into the range formula: \( d = v_{x} \cdot 2.08 \). This will give you the horizontal distance the shot traveled.
Review the steps to ensure all calculations are based on the correct components and formulas. Make sure the trigonometric calculations are accurate and the time of flight is correctly applied to find the horizontal distance.

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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 thrown or projected into the air, subject to only the acceleration of gravity. It involves two components: horizontal and vertical motion. The horizontal motion occurs at a constant velocity, while the vertical motion is influenced by gravity, causing the object to follow a parabolic trajectory.
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Kinematic Equations

Kinematic equations describe the motion of objects in terms of displacement, velocity, acceleration, and time. For projectile motion, these equations help determine the horizontal and vertical components of motion. The horizontal distance can be calculated using the formula: distance = velocity × time, where the horizontal velocity is the initial velocity multiplied by the cosine of the launch angle.
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Components of Velocity

The initial velocity of a projectile can be broken down into horizontal and vertical components using trigonometric functions. The horizontal component (Vx) is found using Vx = V * cos(θ), and the vertical component (Vy) is Vy = V * sin(θ), where V is the initial velocity and θ is the angle of projection. These components are crucial for analyzing the projectile's motion separately in horizontal and vertical directions.
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Related Practice
Textbook Question

In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. What is the height of the shelf above the point where the quarter leaves your hand?

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Textbook Question

In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. What is the vertical component of the velocity of the quarter just before it lands in the dish?

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Textbook Question

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. How far from its firing point does the shell land?

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Textbook Question

A man stands on the roof of a 15.0-m-tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.0° above the horizontal. Ignore air resistance. Calculate Draw x-t, y-t, vx–t, and vy–t graphs for the motion.

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Textbook Question

A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.0° above the horizontal. The shot hits the ground 2.08 s later. Ignore air resistance. What are the components of the shot's velocity at the beginning and at the end of its trajectory?

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Textbook Question

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. At its highest point, find the horizontal and vertical components of its acceleration and velocity.

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