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A soccer ball at rest on the ground, is kicked with an initial velocity of 12.5 m/s at a launch angle of 30 degrees. Calculate its total flight time, assuming that air resistance is negligible.

A soccer ball at rest on the ground, is kicked with an initial velocity of 12.5 m/s at a launch angle of 30 degrees. Calculate its total flight time, assuming that air resistance is negligible.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:** A soccer ball at rest on the ground is kicked with an initial velocity of 12.5 m/s at a launch angle of 30 degrees. Calculate its total flight time, assuming that air resistance is negligible. **Explanation:** To solve this problem, you can use the kinematic equations of motion. The flight time depends on the vertical component of the initial velocity and the acceleration due to gravity. 1. **Calculate the vertical component of velocity (Vy)**: - Vy = 12.5 m/s * sin(30°) = 12.5 * 0.5 = 6.25 m/s 2. **Use the vertical motion formula**: - Total flight time (T) = 2 * Vy / g - Where g = 9.81 m/s² (acceleration due to gravity). 3. **Calculate total flight time**: - T = 2 * 6.25 m/s / 9.81 m/s² = 1.27 seconds The soccer ball will be in the air for approximately 1.27 seconds.
Transcribed Image Text:**Problem Statement:** A soccer ball at rest on the ground is kicked with an initial velocity of 12.5 m/s at a launch angle of 30 degrees. Calculate its total flight time, assuming that air resistance is negligible. **Explanation:** To solve this problem, you can use the kinematic equations of motion. The flight time depends on the vertical component of the initial velocity and the acceleration due to gravity. 1. **Calculate the vertical component of velocity (Vy)**: - Vy = 12.5 m/s * sin(30°) = 12.5 * 0.5 = 6.25 m/s 2. **Use the vertical motion formula**: - Total flight time (T) = 2 * Vy / g - Where g = 9.81 m/s² (acceleration due to gravity). 3. **Calculate total flight time**: - T = 2 * 6.25 m/s / 9.81 m/s² = 1.27 seconds The soccer ball will be in the air for approximately 1.27 seconds.
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