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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
All textbooksYoung & Freedman Calc 14th EditionCh 03: Motion in Two or Three DimensionsProblem 19a
Chapter 3, Problem 19a

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?
A person tossing a quarter at 60° to hit a dish 2.1 m away, aiming to win a stuffed giraffe.

Verified step by step guidance
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First, break down the initial velocity of the coin into its horizontal and vertical components. The horizontal component (v_x) can be found using the formula v_x = v * cos(θ), and the vertical component (v_y) can be found using v_y = v * sin(θ), where v = 6.4 m/s and θ = 60°.
Calculate the time (t) it takes for the coin to travel the horizontal distance to the dish. Use the formula for horizontal motion: distance = v_x * t. Here, the distance is 2.1 m.
Next, use the time calculated to find the vertical displacement of the coin. Apply the kinematic equation for vertical motion: y = v_y * t - (1/2) * g * t^2, where g is the acceleration due to gravity (approximately 9.8 m/s²).
The vertical displacement calculated in the previous step gives the height of the shelf above the point where the quarter leaves your hand.
Ensure all units are consistent and check the calculations for any errors. This will provide the height of the shelf above the initial point.

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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 gravitational forces. It can be analyzed in two dimensions: horizontal and vertical. The horizontal motion is uniform, while the vertical motion is influenced by gravity, leading to a parabolic trajectory. Understanding this concept is crucial for determining the path and landing point of the quarter.
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Introduction to Projectile Motion

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. In this scenario, they can be used to relate the initial velocity, angle of projection, time of flight, and displacement. Specifically, the equations can help calculate the vertical height of the shelf by analyzing the time it takes for the quarter to travel horizontally and the corresponding vertical displacement due to gravity.
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Trigonometric Functions

Trigonometric functions, such as sine and cosine, are essential for resolving the initial velocity of the quarter into its horizontal and vertical components. For an angle of 60°, the horizontal component can be found using cosine, while the vertical component uses sine. These components are vital for applying kinematic equations to find the height of the shelf above the point where the quarter is tossed.
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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 vertical component of the velocity of the quarter just before it lands in the dish?

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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. How far did she throw the shot horizontally?

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Textbook Question

A 124 kg balloon carrying a 22 kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0 kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 5.00 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 20.0 m/s. How high is the balloon when the rock is thrown?

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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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