to start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 290 m/s at 53.0° above the horizontal. it explodes on the mountainside 35.0 s after firing. what are the x and y coordinates of the shell where it explodes, relative to its firing point?

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Louzarym9izzl1edayal Louzarym9izzl1edayal

16-07-2016
Physics

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to start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 290 m/s at 53.0° above the horizontal. it explodes on the mountainside 35.0 s after firing. what are the x and y coordinates of the shell where it explodes, relative to its firing point?

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Abbottboy Abbottboy · Answer 1 · 2016-07-16T04:01:19-04:00

So this is easy to calculate when you split the velocity into x and y components. The x component is going to equal cos(53) 290 and the y component is going to equal sin(53)290.

The x location therefore is 290cos(53)35 = 6108.4m

The y location needs to factor in the downwards acceleration of gravity too, which is 9.81m/s^2. We need the equation dist. = V initialtime + 0.5accelerationtime^2.

This gives us d=290sin(53)35 + (0.5-9.81*35^2)=2097.5m

So your (x,y) coordinates equals (6108.4, 2097.5)