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Ch 03: Motion in Two or Three Dimensions
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 03: Motion in Two or Three DimensionsProblema 16e
Capitolo 3, Problema 16e

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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1
Start by understanding that the shell is subject to projectile motion, which involves both horizontal and vertical components of motion. The acceleration due to gravity acts vertically downward throughout the motion.
At the highest point of the projectile's trajectory, the vertical component of the velocity becomes zero because the shell momentarily stops moving upward before descending. The horizontal component of the velocity remains constant throughout the motion since there is no air resistance.
The horizontal component of the initial velocity can be calculated using the formula: vx=v⁢cos⁢θ, where v is the initial velocity and θ is the angle of projection.
The vertical component of the initial velocity can be calculated using the formula: vy=v⁢sin⁢θ. At the highest point, this component becomes zero.
The acceleration in the horizontal direction is zero because there is no air resistance or other forces acting horizontally. The vertical acceleration is equal to the acceleration due to gravity, which is g=9.8⁢m/s2 downward.

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Projectile Motion

Projectile motion involves the motion of an object thrown into the air, subject to only the acceleration due to gravity. It can be analyzed by breaking it into horizontal and vertical components. The horizontal motion is uniform, while the vertical motion is uniformly accelerated due to gravity.
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Introduction to Projectile Motion

Components of Velocity

The velocity of a projectile can be split into horizontal and vertical components using trigonometric functions. At the highest point, the vertical component of velocity is zero, while the horizontal component remains constant, as there is no air resistance affecting the motion.
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Calculating Velocity Components

Acceleration Due to Gravity

In projectile motion, the only acceleration acting on the object is due to gravity, which is approximately 9.81 m/s² downward. At the highest point of the trajectory, the horizontal acceleration is zero, and the vertical acceleration is equal to the acceleration due to gravity.
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Acceleration Due to Gravity
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