Q1 and 2 are linked and belong to one question A projectile is fired horizontall

Question

Q1 and 2 are linked and belong to one question

A projectile is fired horizontally from some height, y plusminus delta y, and hits the ground a horizontal distance, x plusminus delta x, away. Use the position of impact to calculate the initial velocity, v_0, of the projectile. In other words, find v_0 as a function of x, y and the acceleration due to gravity g. Use error propagation to calculate the uncertainty associated with the initial velocity, delta v_0 in terms of x, y, delta x, and delta y.

Explanation / Answer

1) Here, time taken , t = sqrt(2y/g)

    => initial velocity of projectile , vo =   horizontal distance/time

                                                    =    x/[sqrt(2y/g)]

2)   uncertainty associated with initial velocity =   x(dx)/[sqrt(2ydy/g)]

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