## What equation will be used in this problem?

nixoripavo
Posts: 2
Joined: Mon Jun 18, 2018 6:58 pm

### What equation will be used in this problem?

The statement of this problem stated "A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 352 km/hour at an altitude of 925 m . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80 m/s2 .What is the speed vf of the package when it hits the ground?"

What I have done so far is
t=13.7
x=1340m
Vy(t)=V0y+ayt

I believe that this problem applies to the kinematic equations since its asking for speed. However, I don't see how to find the final speed.

Do I need to upload the picture?

jeff
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

### Re: What equation will be used in this problem?

Hi nixoripavo,
nixoripavo wrote:
Mon Jun 18, 2018 7:00 pm
The statement of this problem stated "A relief airplane is delivering a food package to a group of people stranded on a very small island. The island is too small for the plane to land on, and the only way to deliver the package is by dropping it. The airplane flies horizontally with constant speed of 352 km/hour at an altitude of 925 m . The positive x and y directions are defined in the figure. For all parts, assume that the "island" refers to the point at a distance D from the point at which the package is released, as shown in the figure. Ignore the height of this point above sea level. Assume that the acceleration due to gravity is g = 9.80 m/s2 .What is the speed vf of the package when it hits the ground?"

What I have done so far is
t=13.7
x=1340m
Vy(t)=V0y+ayt

I believe that this problem applies to the kinematic equations since its asking for speed. However, I don't see how to find the final speed.

Do I need to upload the picture?
I think I understand enough so that the picture is not needed. And it looks like you've already done most of the work involved. It looks like you used the vertical equations to find the time (t=13.7 seconds), and then used that and the horizontal speed (vx = 97.78 m/s) to find the horizontal distance travelled. The important thing there is you have the time and the horizontal speed already.

So now in your equation Vy = Voy + ay * t, you have everything to find Vy, right? You know Voy, ay, and t. What does that give you for the final vertical velocity Vy?

And once you have both the horizontal and vertical velocities, we can use the Pythagorean theorem to find the total speed. What do you get for that?

nixoripavo
Posts: 2
Joined: Mon Jun 18, 2018 6:58 pm

### Re: What equation will be used in this problem?

Is V0y=1340?

jeff
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

### Re: What equation will be used in this problem?

nixoripavo wrote:
Mon Jun 18, 2018 8:56 pm
Is V0y=1340?
No, that's the horizontal distance travelled. The initial vertical velocity Voy is the vertical velocity the instant that the crate is released. However, the airplane is moving horizontally, so right when the crate is released, it has no vertical motion, right? So here Voy=0. Does that make sense?

(Of course, it starts falling downwards right away and so gets a vertical velocity, but right at the instant it is released it is only moving horizontally with the plane.)

So with that, and with the vertical acceleration due to gravity ay = -9.8 m/s^2, your equation for the vertical velocity right when it reaches the ground is

Vy = Voy + ay * at
Vy = (0) + (-9.8)*(13.7)
Vy = -134.6 m/s

So when it impacts the ground, it has a horizontal speed of 97.78 m/s, and a vertical speed of 134.6 m/s. And we can combine those using the Pythagorean theorem. What does that give for the final answer?