A shell is fired horizontally from a powerful gun located 144 ft above a horizontal plane ...

A shell is fired horizontally from a powerful gun located 144 ft above a horizontal plane  with a muzzle speed of 800 ft/sec. (a) How long does the shell remain in the air? (b) What is  its range? (c) What is the magnitude of the vertical component of its velocity as it strikes the  target?

Solution

(a) 

Time of flight can be calculated using the vertical motion equation: 

vf = vi + a * t 0 = vi - g * t t = vi / g = 800 / 32.2 = 24.7 sec


(b) 

Range can be calculated using the horizontal motion equation: 

R = vi * t R = 800 * 24.7 = 19,760 ft


(c) 

Vertical component of velocity can be calculated using the vertical motion equation: 

vf = vi + a * t vf = 800 - 32.2 * 24.7 = -188.8 ft/sec 

Magnitude of the vertical component of velocity:

velocity = sqrt(vf^2) = sqrt((-188.8)^2) = 188.8 ft/sec

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