(11%) Problem 3: A baseball slugger slams a pitch and watches the ball sail into

Question

(11%) Problem 3: A baseball slugger slams a pitch and watches the ball sail into the bleachers for a home run, landing h- 7.5 m higher than it was hit. When visiting with the fan that caught the ball, he learned the ball was moving with final velocity 37.8 m/s at an angle 6 26 below horizontal when caught. Assume the ball encountered no air resistance, and use a Cartesian coordinate system with the origin located at the ball's initial position. 0, Otheexpertta.com 25% Part (a) Create an expression for the ball's initial horizontal velocity, vor in terms of the variables given in the problem statement. Grade Summary Deductions Potential 0% 100% cos(a) cos(( Submissions Attempts remaining: (2% per attempt) detailed view sin a) sin(sin(e) NO Submit Hint I give up Hints: 200 deduction per hint. Hints remaining: 3 Feedback: 0% deduction per feedback. 2596 Part (b) Calculate the ball's initial vertical velocity, var in ms 25% Part (c) Calculate the magnitude of the ball's initial velocity, vo-in ms. 25% Part (d) Find the angle 0 in degrees above the horizontal at which the ball left the bat. All content 2018 Expert TA. LLC

Explanation / Answer

here,

h = 7.5 m

initial speed , u = 37.8 m/s

thetaf = 26 degree

a)

the ball's initial horizontal velocity , ux = u * cos(theta)

ux = 37.8 * cos(26) m/s

ux = 34 m/s

b)

the ball's initial vertical velocity be vy

using third equation of motion

vy^2 - uy^2 = 2 * g * h

(v * sin(theta))^2 - ( uy^2) = - 2 * 9.81 * 7.5

(37.8 * sin(26))^2 - ( uy^2) = - 2 * 9.81 * 7.5

solving for uy

uy = 20.5 m/s

c)

the magnitude of the initial velocity , |u| = sqrt(ux^2 + uy^2)

|u| = sqrt(34^2 + 20.5^2) = 39.7 m/s

d)

theta = arctan(uy/ux)

theta = arctan(20.5/34) = 31.1 degree counter clockwise from +x axis

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