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1-3. A ball is thrown from a tower shown in the figure. If the initial velocity is 25 ft/s. (1) Determine the x and y coordinates where the ball strikes the slope. Assume x A = 35 ft . (2) If x A is a random variable and follows a normal distribution x A N (35, 32 ) ft , calculate the probability that the ball will not hit the slope. 25 ft/s 5 4 3 60 ft 1 3 35 ft Solution (1) Assume the ball hits the slope. Since = s s0 + v0t , we have x x0 + v0 cos θ t = 3 0 + 25 t = 15t = 5 1 y= y0 + v0 sin θ t + at 2 2 4 1 = 60 + 25 t + ( −32.2)t 2 = 60 + 20t − 16.1t 2 5 2 The equation of the slope is y − y A = k ( x − x A ) where ( x A , y A ) = (35,0) ft and k = 1 / 3 , and therefore = y 1 ( x − 35) 3 60 + 20t − 16.1t 2= 1 (15t − 35) 3 Solving the equations above and choosing the positive root yields t = 2.6265 s thus = x 15 = t 15(2.6265) = 39.397 ft y= 1 1 ( x − 35) = (39.397 − 35) = 1.466 ft 3 3 Therefore, the coordinates are ( x, y ) = (39.397,1.466) ft . Ans. (2) When x A N (35, 32 ) ft , the probability that the ball will not hit the slope x − µ xA P( x < x A ) = 1 − P( x A < x ) = 1 − Φ σx A 39.379 − 35 = 1− Φ 3 = 0.0714 Therefore, the probability that the ball will not hit the slope is 0.0714. Ans.