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(20%) A very small ball is held by a man at (0, 0, H), that is, at a height H above the ground. The horizontal position of the ball is measured to an accuracy ofAxThe ball is then let go to vertically hit the ground at (0, 0, 0). Estimate the minimal miss distance on the ground from (0, 0, 0). 4.

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Given Data Height of the ball, H Accuracy of measurement of horizontal position. ± Διο Initial speed of the ball, u0 Write the expression for the time to reach the ground from (0,0,H) to (0,0,0) Here, the time required is t, the initial velocity in the y direction is u and the acceleration due to gravity is g Substitute the given values in the above expression. 2H Write the expression for horizontal distance covered by the ball at ground (0,0,0)Here, the initial velocity in the horizontal direction at release is u 2H Substitutefor t in the above expression 2H Write the expression for variation in the measurement in the measurement of horizontal distance Here, the new distance is x Since the initial position of the ball is zero so, Substitute the given values in the above expression For the minimal miss distance take the negative sign in the above expression2H1 g 2 2V g lu 2g Thus, the minimal miss distance is u 2

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