Question

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.

Answer 1

Answer:

$s=274.2857\ m$ is the distance from the target before which the pilot must release the canister.

Explanation:

Given:

• height of the plane, $h=90\ m$

• horizontal speed of plane, $v_x=64\ m.s^{-1}$

Time taken by the canister to hit the ground:

using equation of motion

$h=u_y.t+\frac{1}{2} g.t^2$

where:

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

$t=$ time taken to hit the ground

$90=0+0.5\times 9.8\times t^2$

$t=4.2857\ s$

Now the horizontal distance travelled by the canister after dropping:

$s=v_x\times t$

$s=64\times 4.2857$

$s=274.2857\ m$ is the distance from the target before which the pilot must release the canister.