Question

A baseball slugger hits a pitch and watches the ball fly into the bleachers for a home run, landing h=8.5 m higher than it was struck. When visiting with the fan that caught the ball, he learned the ball was moving with final velocity vf= 39.45 m / s at an angle θf=29.5° 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.

Answer 1

a)

V0x = Vf cos(theta)

b)

V0x = Vf cos(theta)

= 39.45 m/s x cos29.5

= 34.335 m/s

tan(theta) = Vy/Vx

Vy = Vx tan(theta)

Vy = 34.335 m/s  x tan(-29.5)

= -19.426 m/s

From kinematic equation ,Vy^2 =V0y^2 + 2 a S

V0y = sqrt (Vy^2 + 2 a S)

Voy = sqrt ((-19.426)^2 + 2 x 9.80 x 8.5)

=23.32 m/s

Hence, V0y = 23.32 m/s

c)

V0 = Voy/sin(theta)

= (23.32 m/s)/sin29.5

= 47.36 m/s

Hence, V0 = 47.36 m/s

d)

theta = tan- (23.32/34.335) = 34.2 deg

Hence, theta = 34.2 deg