A cannon situated on the top of a tower of height H=50 m fires a cannon ball at

Question

A cannon situated on the top of a tower of height H=50 m fires a cannon ball at a angle of 30 degree to the horizontal. The cannon ball leaves the cannon at a speed of 200 m/s. Write down equations for x and y coordinates of the cannon ball as functions of time (take g=9.8 m/s) How long is the cannon ball in the air before hitting the ground ? How far horizontally has it traveled by the time it hits the ground ? What is the maximum height attained by the cannon ball ? The cannon is now aimed vertically. What is the smallest initial speed for the cannon ball that would allow it to escape from the gravitational field of the Earth the radius of the Earth as and the mass of Earth to be) ?

Explanation / Answer

E)    Applying conservation of energy =>

    Here,    1/2* m * v2 = GMm/r

=>        0.5 * v2 = (6.67 * 10-11 * 5.98 * 1024/6.4 * 106)

=>     v = 11164.48 m/sec

              =   11.164 km/sec

=> smallest initial speed =    11.164 km/sec   =   11164.48 m/sec

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