Vector in two dimension?

Question

an artillery shell is fired with an initial velocity of 300m/s at 55 degree above the horizontal. To clear an avalanche it explodes on a mountainside 42 s after firing. What are the x and y coordinates of the shell where it explodes, relative to its firing point?

Answer 1

Find the vertical initial velocity,

x= (300) ^ sin 55 = 245.75 ms*-1

vertical position = (245.75)^(42) + (-9.81)^(42)*2 = -6983.34 m

Find the horizontal initial velocity,

y= (300) ^ cos 55 = 172.07 ms*-1

horizontal position = (172.07)^(42) = 7226.94 m

therefore,

coordinate = ( 7226.94 , -6983.34 )