To start an avalanche on a mountain slope, an artillery shell is fired with an initial velocity of 310 m/s at 57.0° 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?
x=? (m)
y=? (m)
SOLUTION :
Shell is fired at an angle of 57º and speed of 310 m/s.
upward. It travels for 37 seconds and explodes.
So,
horizontal speed of shell , Vh = 310 cos (57) = 168.8381 m/s
vertical speed of shell , Vv = 310 sin (57) = 259.9879 m/s
Coordinates of explosion point relative to firing point(0, 0) :
X = Horizontal distance moved by shell = Horizontal speed * time
= 168.8381 * 37 = 6247.00 meters
Y = vertical distance travelled by shell
= u t - 1/2 g t^2 ; (u = Vv)
= (259.9879)(37) - 1/2 * 9.8 * (37)^2 = 2911.45 meters.
Hence, X, Y coordinates of explosion point are : 6247.00 m and 2911.45 m respectively.
(ANSWER).
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