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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 18b
Capitolo 3, Problema 18b

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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To find the components of the shot's initial velocity, we need to resolve the velocity vector into horizontal and vertical components using trigonometric functions. The initial velocity is given as 12.0 m/s at an angle of 51.0° above the horizontal.
The horizontal component of the initial velocity (v_x) can be found using the cosine function: v_x = v * cos(θ), where v is the initial velocity and θ is the angle. Substitute the given values: v_x = 12.0 m/s * cos(51.0°).
The vertical component of the initial velocity (v_y) can be found using the sine function: v_y = v * sin(θ). Substitute the given values: v_y = 12.0 m/s * sin(51.0°).
To find the components of the shot's velocity at the end of its trajectory, we need to consider the effect of gravity on the vertical component. The horizontal component remains unchanged as there is no air resistance. The final vertical velocity (v_y_final) can be calculated using the equation: v_y_final = v_y_initial - g * t, where g is the acceleration due to gravity (9.8 m/s²) and t is the time (2.08 s).
The final horizontal component of the velocity (v_x_final) is the same as the initial horizontal component since there is no air resistance: v_x_final = v_x_initial. Therefore, the final velocity components are v_x_final and v_y_final.

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Projectile motion involves the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. It is characterized by a parabolic trajectory due to the influence of gravity acting downward, while the initial velocity has both horizontal and vertical components.
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Velocity components refer to the breakdown of a vector into its horizontal and vertical parts. For a projectile, the initial velocity can be split into horizontal (vx = v * cos(θ)) and vertical (vy = v * sin(θ)) components, where v is the magnitude of the velocity and θ is the angle of projection.
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