How Do You Calculate the Time and Distance of a Crate in Freefall from a Plane?

[Mr Matt]

Homework Statement

A cargo plane flying horizontally at an altitude of 13.9 km with a constant speed of 508 km/hr when a large crate slides out of the rear of the plane
Assume the acceleration of gravity is 9.81 meters/seconds squared.

1)How long does it take for the crate to hit the ground?
2)What is the horizontal distance of the crate from the point it fell off to the point where it hits the ground?
3)How far is the crate from the airplane when the crate hits the ground assuming the plane remains at a constant speed?

Homework Equations

The golden three:

Vf = Vi + (A)(T)
Vf^2 = Vi^2 + 2(A)(D)
D = (Vi)(T) + 1/2(A)(T^2)
(sorry i don't know how to do the squared simbol)

The Attempt at a Solution

First, I drew a diagram of what is described in the problem. We were also talk to make a chart and fill in the values. Once i know what the values are for the charts, i will be able to solve the problem(it is multiple parts). I only need help in solving the values for the charts. The chart is as follows:

Vertical(y)__________Horizontal(x)
Vi- 0 ______________Vx- ?
Vf- ? ______________Dx- ?
A-(-9.8m/s)_________T-?
D- 13.9km
T-?

I know that time is constant on both, and i think i have all the given info in the charts, but i don't really know what to do after this. Please, if anyone could help that would be great, thanks

 

[cristo]

How about using equation number 3 to solve for time using the vertical components.

You have said that vi in the y direction is 0. Does this tell you anything about vi in the x direction?

 

[Mr Matt]

But i don't know if you use the vertical or horizontal equations, and I think Vx might be 508 km/hr, but its just a guess. Can anyone confirm this?

 

[cristo]

But i don't know if you use the vertical or horizontal equations,

Like I said above, use your third equation in the vertical direction to solve for t.

and I think Vx might be 508 km/hr, but its just a guess. Can anyone confirm this?

vi in the x direction = 508 km/h. Note that you should have vi and vf in the x direction, like in the y direction, not just one term vx.

I suggest you use obtain t in the y direction, and then you should be able to solve the other problems using this t (since equal time will be taken for the crate to fall in both the x and y directions).

 

[Mr Matt]

I suggest you use obtain t in the y direction, and then you should be able to solve the other problems using this t (since equal time will be taken for the crate to fall in both the x and y directions).

kk thanks a lot

 

[Mr Matt]

But then how would u solve for the third question? The third question isn't a variable in one of the following equations right? I'm so confused :(

 

[cristo]

But then how would u solve for the third question? The third question isn't a variable in one of the following equations right? I'm so confused :(

Presume the plane traveling at constant horizontal velocity. You know the time the crate hits the ground, so calculate the distance the plane travels in this amount of time. Subtract from this the distance from the intial point that the crate hits the ground.