Calculating Horizontal Distance and Time for a Package Ejected from a Plane

In summary, the conversation discusses the time it takes for a package ejected from a plane to reach sea level and the horizontal distance the package should be released from the plane to land on an island. The equations used to solve these problems are X=Vix*T, Vfx=Vix+a*t, Vfx^2=Vix^2+2*a*x, y=vi*t+0.5a*t^2, Vf=Vi+a*t, and vfy^2=Viy^2+2a*y. After some calculations, the time is found to be 12.8 seconds and the horizontal distance is 1256 meters. The mistake of using 200 mph instead of 220 mph is corrected
  • #1
tater08
29
0

Homework Statement


After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 220 mph in the horizontal direction.

If the package is to land right on the island, at what horizontal distance D from the plane to the island should the package be released?


2. Homework Equations

X=Vix *T + 0.5 *at^2 = X=Vix*T
Vfx=Vix+a*t
Vfx^2=Vix^2 + 2*a*x

y=vi*t+0.5a*t^2
Vf=Vi+a*t
vfy^2=Viy^2+2a*y

The Attempt at a Solution



I ended solving for the first part that is looking fro time which was 12.8 sec. For the second part, i converted the 200 mph into 89.41 m/s. I then used the X=Vi *t equation. X=89.41 m/s * 12.78sec = 1142.67 m. But somehow it is the wrong answer. I do not know where else to go. Please help! Thanks
 
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  • #2
tater08 said:

Homework Statement


After a package is ejected from the plane, how long will it take for it to reach sea level from the time it is ejected? Assume that the package, like the plane, has an initial velocity of 220 mph in the horizontal direction.

If the package is to land right on the island, at what horizontal distance D from the plane to the island should the package be released?


2. Homework Equations

X=Vix *T + 0.5 *at^2 = X=Vix*T
Vfx=Vix+a*t
Vfx^2=Vix^2 + 2*a*x

y=vi*t+0.5a*t^2
Vf=Vi+a*t
vfy^2=Viy^2+2a*y

The Attempt at a Solution



I ended solving for the first part that is looking fro time which was 12.8 sec. For the second part, i converted the 200 mph into 89.41 m/s. I then used the X=Vi *t equation. X=89.41 m/s * 12.78sec = 1142.67 m. But somehow it is the wrong answer. I do not know where else to go. Please help! Thanks


Your original problem says 220 mph not 200 mph.

Your altitude is not given.
 
  • #3
oops my bad, the altitude is 800 meters and the new x in meters is 1256 meters. sorry about the mixup
 
  • #4
tater08 said:
oops my bad, the altitude is 800 meters and the new x in meters is 1256 meters. sorry about the mixup

Plug in your new numbers. That's probably all it is.

Good Luck.
 

1. What is horizontal projection?

Horizontal projection is a method used in science and mathematics to determine the position of an object at a specific time. It involves analyzing the horizontal motion of an object and predicting its future position based on its initial velocity and acceleration.

2. What is the difference between horizontal projection and vertical projection?

The main difference between horizontal projection and vertical projection is the direction of the motion being analyzed. Horizontal projection focuses on the motion of an object along the horizontal axis, while vertical projection focuses on the motion along the vertical axis.

3. How is horizontal projection used in real life?

Horizontal projection is commonly used in physics, engineering, and other scientific fields to predict the trajectory of moving objects. It is also used in sports, such as in the analysis of the trajectory of a baseball or basketball.

4. What are the key components of horizontal projection?

The key components of horizontal projection include the initial velocity of the object, the angle at which it is projected, and the acceleration acting on the object. These factors determine the path of the object and its position at any given time.

5. How is horizontal projection calculated?

To calculate horizontal projection, you can use the equation x = v₀t + 1/2at², where x is the horizontal distance traveled, v₀ is the initial velocity, t is time, and a is acceleration. Alternatively, you can use trigonometric functions to determine the horizontal and vertical components of the object's motion.

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