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In fighting forest fires, airplanes work in support of ground crews by dropping water on the fires. For practice, a pilot drops a canister of red dye, hoping to hit a target on the ground below. If the plane is flying in a horizontal path 90.0 m above the ground and has a speed of 64.0 m/s (143 mi/h), at what horizontal distance from the target should the pilot release the canister? Ignore air resistance.

Respuesta :

Answer:

[tex]s=274.2857\ m[/tex] is the distance from the target before which the pilot must release the canister.

Explanation:

Given:

  • height of the plane, [tex]h=90\ m[/tex]
  • horizontal speed of plane, [tex]v_x=64\ m.s^{-1}[/tex]

Time taken by the canister to hit the ground:

using equation of motion

[tex]h=u_y.t+\frac{1}{2} g.t^2[/tex]

where:

[tex]u_y=[/tex] initial vertical velocity of the canister = 0 (since the the object is dropped from a horizontally moving plane)

[tex]t=[/tex] time taken to hit the ground

[tex]90=0+0.5\times 9.8\times t^2[/tex]

[tex]t=4.2857\ s[/tex]

Now the horizontal distance travelled by the canister after dropping:

[tex]s=v_x\times t[/tex]

[tex]s=64\times 4.2857[/tex]

[tex]s=274.2857\ m[/tex] is the distance from the target before which the pilot must release the canister.

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