Problem 12107 Part A The golf ball is hit at A with a speed

Problem 12.107 Part A The golf ball is hit at A with a speed of UA = 32 m/s and directed at an angle of 30° with the horizontal as shown (Figure 1) Determine the distance d where the ball strikes the slope at B Express your answer to three significant figures and include the appropriate units. d Value Units Submit My Answers Give Up Continu Figure 1 1of1

Solution

first I split the speed vector in horizontal and vertical speeds
vx_0 = 32 * cos (30°) = 16 * sqrt(3)
vy_0 = 32 * sin (30°) = 16

vy = vy_0 - gt (vertical speed in time t)
vx = vx_0 (horizontal -||-)

y = vy_0t - 1/2 * gt^2 (heigth in time t)
x = vx*t (distance in time t)

y = x/5 (the slope)

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vx/5 = vy_0 - 1/2gt
t = (vy_0 - vx/5)*2/g (time, when the ball hits the slope)
x = vx*(vy_0 - vx/5)*2/g = 32 * sqrt(3) * (16 - (16/5)*sqrt(3)) / 9.84 = 58.9 distance units