A target plane flies at 2100 meters. An antiaircraft gun fires a projectile with an initial upward velocity of 200 m/sec. Will the projectile ever reach the altitude of the target plane?

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Answer 1 · 2016-03-25T14:06:10

NO, because Maximum height is only
#s=2,040.82" "#meters

From the given : height of the plane#=2100# meters

From Physics, #s=v_o *t+1/2*g*t^2# and #v_o=200" "m/sec#
The #g=-9.8 " "##m/sec^2#(negative because accelaration due to gravity is directed downward)

#s=v_o *t+1/2*g*t^2#

#s=200*t+1/2*-9.8*t^2#

To determine the maximum, we convert this parabolic equation to its Vertex Form by completing the square

#s=-9.8/2*t^2+200t#

#s=-9.8/2(t^2-400/9.8*t)#

#s=-9.8/2(t^2-400/9.8*t+(200/9.8)^2-(200/9.8)^2)#

#s=-9.8/2(t-200/9.8)^2+9.8/2*(200/9.8)^2#

simplify first

#s=-9.8/2(t-200/9.8)^2+20000/9.8#
#s-20000/9.8=-9.8/2(t-200/9.8)^2#

#(t-200/9.8)^2=-2/9.8(s-20000/9.8)#

This is the vertex form #(x-h)^2=-4p(y-k)#

Maximum #s=20000/9.8=2040.82" "#meters

This is not enough to hit the plane at 2100 meters

God bless.... I hope the explanation is useful.