exploding shell?
A 44-kg shell is fired from a gun with a muzzle velocity 120 m/s at 57° above the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. Calculate the range of the other fragment, assuming level terrain.
First, find the distance traveled to explosion and height of explosion
when vy=0, apogee
vy(t)=120*sin(57)-9.81*t
t=10.26 seconds
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the distance to that point is
120*cos(57)*10.26
670.5 m
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and the height will be
y(t)=120*sin(57)*t-.5*9.81*t
516.23 m
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at that moment the explosion occurs and
120*cos(57)=v/2
solve for v, which is the horizontal speed of the fragment
130.7 m/s
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The fall time will be
10.26
the additional range will be
130.7*10.26
1341 m
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total range
2011.5 m
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