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

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

Step-by-step 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+(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* 9.8* t^2`

`t=4.2857\ s`

Now the horizontal distance travelled by the canister after dropping:

`s=v_x* t`

`s=64* 4.2857`

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