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To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 310 m/s at 58.0° above the horizontal. It explodes on the mountainside 37.0 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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You are given the time so that is nice. Y= Y(0)+V(y0)t-(1/2)gt y(0) is zero. V(y0) is 310sin(58) = 262.9(37) -(1/2)(9.80)(37)=9546 meters in the air for Y. X=x(0) +V(x0)t x(0) is zero. V(x0)=310cos58=164.3(37)=6078 meters traveled horizontally.
Therefore coordinate system is (6078,9546). Im a little rusty.
Isn't the equation gt^2?

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Yes it is. Im so sorry. However, I'm glad you knew what you were doing and actually spotted that mistake. :)

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