A football player launches the ball from initial position x(0)=y(0)=0, with initial velocity v = v, cos 8 î + v, sin 0j. Neglecting drag, the ball's trajectorydescribes a parabola in the Oxy plane, where y is the vertical upward direction and x is the horizontal direction. After a distance d along the x-direction, theball returns to the ground at y=0. (a) Find a formula for vo as a function of the angle 0 and the distance d. (b) Assuming d = 49 m, 0 = 45°, find the time ittakes for the ball to return to the ground. (c) Now, consider drag. The drag force is F = -bv, with b-constant. Find a formula for the horizontal distancetraveled by the ball, Xh, when the ball reaches maximum height, y(xn)=ymax; Xh should be expressed as a function of b, g, vo, 0, and the ball's mass m.

Name: A football player launches the ball from initial position x(0)=y(0)=0
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Description: A football player launches the ball from initial position x(0)=y(0)=0, with initial velocity v = v, cos 8 î + v, sin 0j. Neglecting drag, the ball's trajectorydescribes a parabola in the Oxy plane, where y is the vertical upward direction and x is t

v = v0cosθi^+v0sinθj^Gravitational force = -mgj^

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A football player launches the ball from initial position x(0)=y(0)%=D0, with initial velocity v = v, cos 0 i + vo sin 0j. Neglecting drag, the ball's trajectory describes a parabola in the Oxy plane, where y is the vertical upward direction and x is the horizontal direction. After a distance d along the x-direction, the ball returns to the ground at y=D0. (a) Find a formula for vo as a function of the angle 0 and the distance d. (b) Assuming d = 49 m, 0 = 45°, find the time it takes for the ball to return to the ground. (c) Now, consider drag. The drag force is F = -bv, with b=constant. Find a formula for the horizontal distance traveled by the ball, Xh, when the ball reaches maximum height, y(xh)=Vmaxi Xh should be expressed as a function of b, g, Vo, 0, and the ball's mass m.

A football player launches the ball from initial position x(0)=y(0)%=D0, with initial velocity v = v, cos 0 i + vo sin 0j. Neglecting drag, the ball's trajectory describes a parabola in the Oxy plane, where y is the vertical upward direction and x is the horizontal direction. After a distance d along the x-direction, the ball returns to the ground at y=D0. (a) Find a formula for vo as a function of the angle 0 and the distance d. (b) Assuming d = 49 m, 0 = 45°, find the time it takes for the ball to return to the ground. (c) Now, consider drag. The drag force is F = -bv, with b=constant. Find a formula for the horizontal distance traveled by the ball, Xh, when the ball reaches maximum height, y(xh)=Vmaxi Xh should be expressed as a function of b, g, Vo, 0, and the ball's mass m.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter2: Newtonian Mechanics-single Particle

Section: Chapter Questions

Problem 2.3P: If a projectile is fired from the origin of the coordinate system with an initial velocity υ0 and in...

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