The latest Hollywood blockbuster is filming its climatic ending in an abandoned

Question

The latest Hollywood blockbuster is filming its climatic ending in an abandoned city. The hero trapped in a high-rise and surrounded by an evil horde of zombies,fires a cannon that sets off a chain reaction of explosions wiping out zombies. due to the high cost of production the timing for this sequence needs to be perfect. The projectile was fired parallel to the ground has a mass of 467 ± 17g. From a height of 19.58 ± 0.057m it travels horizontally 40.48 ± 3.3m to the target. Using the latest scientific data the special effects team finds that the measured gravitational acceleration for their area is 9.78 ± 0.02 m/s2. Using this information, answer the following questions.

What are the fractional errors of the mass, the horizontal and vertical distances,gravity and time?

Explanation / Answer

For vertical motion, u=0, Therefore, H=(g*t^2)/2. or, t=sqrt(2*H/g)..........(1) Uncertanity for general term like P=(a*b)/c [Let ?represent uncertainty] so, For t, ..........(2) Using (1), t = 4.004 [Use only the exact values to calculate the time and note answer upto the decimal that has same significant values as the datas in the question, here 4.] Put, t, ?H, ?g, H, g in equation (2) and find ?t = 0.009922 sec = 0.01 sec.... I could find the use of datas like mass and horizontal range (without being given the value of initial velo.)

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