1-3. A ball is thrown from a tower shown in the figure. If the initial velocity is 25 ft/s.

(1) Determine the  and  coordinates where the ball strikes the slope. Assume .

(2) If  is a random variable and follows a normal distribution , calculate the probability that the ball will not hit the slope.

Solution

(1) Assume the ball hits the slope.

Since , we have

The equation of the slope is

where  and , and therefore

Solving the equations above and choosing the positive root yields

thus                                                                      

Therefore, the coordinates are .           Ans.

(2) When , the probability that the ball will not hit the slope

Therefore, the probability that the ball will not hit the slope is 0.0714.           Ans.