A baseball slugger smacks a pitch and watches the ball drift into the bleachers

Question

A baseball slugger smacks a pitch and watches the ball drift into the bleachers for a home run. landing A = 6.5 m higher than it was hit. When visiting with the fan that caught the ball, he learned the ball was moving with final velocity v_f= 31.05. m/s at an angle theta_f= 28.5degree 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. Create an expression for the ball's initial horizontal velocity, V_0X, in terms of the variables given in the problem statement. Select from the variables below to write your expression. Note that all variables may not be required. Calculate the ball's initial vertical velocity, V_0y, in m/s. Numeric: A numeric value is expected and not an expression. Calculate the magnitude of the ball's initial velocity, V_0, in m/s. Numeric: A numeric value is expected and not an expression. Find the angle Theta_0 in degrees above the horizontal at which the ball left the bat Numeric: A numeric value is expected and not an expression.

Explanation / Answer

a) vox = vfx

= vf*cos(theta_f)

b) vfy^2 - voy^2 = -2*g*h

voy^2 = vfy^2 + 2*g*h

voy = sqrt(vfy^2 + 2*g*h)

= sqrt( (31.05*sin(28.5))^2 + 2*9.8*6.5)

= 18.6 m/s

c) vox = 31.05*cos(28.5)

= 27.3 m/s

so, vo = sqrt(vox^2 + voy^2)

= sqrt(27.3^2 + 18.6^2)

= 33 m/s

d) theta_o = tan^-1(Voy/Vox)

= tan^-1(18.6/27.3)

= 34.3 degrees

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