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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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

Explanation:

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.

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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?

1 Answer

Explanation:

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