Artillery Shell

To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 300mm/s?

To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 300meter per seconds at 55 degrees above the horizontal. It explodes on the mountain side 42 seconds after firing. What are the x and y coordinatesof the shell where it explodes, relative to its firing point?

I would like to figure out the time for the shell to reach its maximum height first.

Formula is

T = Vo(sin A)/g

where

T = time to reach maximum height
Vo = initial velocity = 300 m/sec.
A = angle of launch = 55 degrees
g = acceleration due to gravity = 9.8 m/sec^2

Substituting values,

T = 300 * sin 55/9.8

T = 25.08 sec.

This means that the shell exploded on its way down. It travelled another 16.92 sec (42 - 25.08) on the way down before exploding.

Maximum vertical height attained by shell = Vo^2(sin^2A)/2g

and substituting values,

H = (300^2)(sin^2 (55))/(2 * 9.8)

H = 3081.17 meters

So, coming down for 16.92 sec., the shell vertical distance from the ground is

S = 3081.17 - (1/2)(gT^2)

S = 3081.17 - (1/2)(9.8)(16.92^2)

S = 3081.17 - 1402.80

S = 1678.37 m

The horizontal displacement of the shell after 42 seconds = (300)*(cos 55)*(42) = 7227.06

ANSWER: After 42 seconds from being launched, the x and y coordinates of the shell (where the origin is its firing point) are

7227.06 meters and 1678.37 meters, respectively.

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