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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
All textbooksGiancoli Douglas 5th editionCh. 03 - Kinematics in Two or Three Dimensions; VectorsProblem 23a
Chapter 3, Problem 23a

A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). What is the vertical component of her acceleration?
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Verified step by step guidance
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Identify the given values: The acceleration of the skier down the hill is 1.80 m/s², and the angle of the hill with respect to the horizontal is 30.0°.
Understand the problem: The vertical component of the acceleration is the portion of the skier's acceleration that acts in the vertical direction (perpendicular to the horizontal). This can be determined using trigonometry.
Use the sine function to find the vertical component of the acceleration. The relationship is given by: avertical = atotal ⋅ sin(θ), where atotal is the total acceleration (1.80 m/s²) and θ is the angle of the hill (30.0°).
Substitute the known values into the equation: avertical = 1.80 ⋅ sin(30.0°). Note that the sine of 30.0° is a known trigonometric value.
Simplify the expression to find the vertical component of the acceleration. Ensure the units remain consistent (m/s²).

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Key Concepts

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

Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. In this context, it refers to the skier's change in speed as she moves down the hill. The acceleration can be influenced by various factors, including gravity, friction, and the incline of the hill.
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Intro to Acceleration

Components of Acceleration

When dealing with inclined planes, acceleration can be broken down into components: vertical and horizontal. The vertical component is influenced by gravity and the angle of the incline, while the horizontal component relates to the skier's movement along the slope. Understanding these components is essential for analyzing motion on an incline.
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Trigonometric Functions

Trigonometric functions, such as sine and cosine, are used to relate the angles of a triangle to the ratios of its sides. In this scenario, the vertical component of the skier's acceleration can be calculated using the sine function, which helps determine how much of the total acceleration acts in the vertical direction based on the angle of the hill.
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Related Practice
Textbook Question

A stunt driver wants to make his car jump over 8 cars parked side by side below a horizontal ramp (Fig. 3–46). With what minimum speed must he drive off the horizontal ramp? The vertical height of the ramp is 1.5 m above the car roofs and the horizontal distance he must clear is 22 m. 

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Textbook Question

A car is moving with speed 16.0 m/s due south at one moment and 25.7 m/s due east 8.00 s later. Over this time interval, determine the magnitude and direction of (a) its average velocity, (b) its average acceleration. (c) What is its average speed? [Hint: Can you determine all these from the information given?]

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Textbook Question

Two vectors, V⃗1\(\vec{V}\)_1 and V⃗2\(\vec{V}\)_2, add to a resultant V⃗R=V⃗1+V⃗2\(\vec{V}\)_R = \(\vec{V}\)_1 + \(\vec{V}\)_2. Describe V⃗1\(\vec{V}\)_1 and V⃗2\(\vec{V}\)_2 if VR2=V12+V22V_R^2 = V_1^2 + V_2^2.

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Textbook Question

A skier is accelerating down a 30.0° hill at 1.80 m/s² (Fig. 3–42). How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation change is 125 m? 

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Textbook Question

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?

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