Answer:
S_y, plate = -0.5325 ft (further away from batter)
Step-by-step explanation:
Given:
V_0 = < 130 , 0 , -3 > ft / s
a = < 0 , 32 , 8 > ft / s^2
S_plate = < 60 , z , 0 > ft
S_0 = < 0 , 6 , 0 > ft
The time taken t by the ball to reach home plate:
S_x, plate = S_o,x + V_o,x * t
60 = 0 + 130*t
t = 60 / 130
t = 0.4615 s
The distance traveled by the ball in y-direction when it reaches home plate at t = 6 / 13 s:
S_y, plate = S_o,y + V_o,y * t + 0.5*a_y*t^2
S_y, plate = 0 -3*(0.4615) + 0.5 * 8 * (0.4615)^2
S_y, plate = -0.5325 ft
