Solve Plane Problem: Find Time & Distance for Dropping Supply Crate

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In summary, the conversation discusses a problem where an airplane is dropping a supply crate from a specified altitude and speed to hit a target. The conversation provides two questions, one asking for the time before the crate should be dropped to hit the target and the other asking for the horizontal distance between the plane and the target when the crate should be dropped. The solution involves converting the speed into m/s and using the formula v=x/t to find the unknowns. It is then clarified that the correct procedure is to find the time in the y direction using the formula d = 1/2gt^2 and then using that time to solve for the horizontal distance using the formula x = vt. The final answers are determined to be 102.14
  • #1
leftyguitarjo
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Homework Statement


An airplane is traveling at 125km/h at an altitude of 1001m. It is dropping a supply crate on a specified target. Air resistance is ignored.

a.)How many seconds before being directly overhead should the box be dropped to hit the target?

b.)What is the horizontal distance between the plane and the target when the box should be dropped?


Homework Equations


velociy in the X direction=x/t


The Attempt at a Solution


I converted the speed into m/s, which came out to be 34.7m/s, which gave me my two unknowns: 34.7=x/t

I decided to find the time in the y (vertical) direction first, using simply 9.8t=1001. t=102.14 seconds. Since the X and Y direction times are the same, I plugged in the time into 34.7=x/t and solved for x an got 3544.26m

And to clarify my answers a.) 102.14 seconds, b.) 3544.26m

I just want to make sure I followed the correct procedure when solving this problem
 
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  • #2
leftyguitarjo said:
I decided to find the time in the y (vertical) direction first, using simply 9.8t=1001.
You are saying that y = gt? That's incorrect. (Perhaps you're mixing it up with v = gt.) Find the correct expression for distance as a function of time for a falling body.
 
  • #3
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Your approach to solving this plane problem is correct. By converting the speed from km/h to m/s, you were able to use the equation for velocity in the X direction to find the time needed for the supply crate to reach the target. Then, using the equation for the vertical motion of an object, you were able to find the time in the Y direction. Since the time in both directions is the same, you were able to solve for the horizontal distance using the same time value. Your final answers of 102.14 seconds and 3544.26m are correct. Great job!
 

What is the purpose of solving a plane problem to find time and distance for dropping a supply crate?

The purpose of solving this type of plane problem is to determine the most efficient and accurate way to drop a supply crate from a plane. This involves calculating the time and distance needed for the crate to reach its target location, taking into consideration factors such as wind speed, air resistance, and gravity. Solving this problem ensures that the supply crate will land at the desired location and time, saving time and resources.

What are the key components involved in solving a plane problem to find time and distance for dropping a supply crate?

The key components involved in solving this type of problem include the initial height and velocity of the plane, the target location and time, and the environmental factors such as wind speed and air resistance. These variables must be accurately measured and entered into the appropriate equations to determine the time and distance needed for the crate to reach its target.

What equations or formulas are used to solve a plane problem to find time and distance for dropping a supply crate?

The equations used to solve this type of problem include the kinematic equations of motion, which take into account the initial velocity, final velocity, acceleration, and time. These equations can be modified to incorporate environmental factors such as wind resistance and air density. Other equations, such as the Pythagorean theorem, may also be used to calculate the distance and trajectory of the crate.

How do environmental factors, such as wind speed, affect the time and distance for dropping a supply crate from a plane?

Environmental factors, such as wind speed, can significantly impact the time and distance needed for the supply crate to reach its target. Wind speed can either increase or decrease the speed at which the crate travels, as well as alter its trajectory. Therefore, it is crucial to accurately measure and account for these factors in the calculations to ensure the crate reaches its intended destination.

What are some methods for validating the accuracy of the calculated time and distance for dropping a supply crate from a plane?

One method for validating the accuracy of the calculations is to compare the results with real-world data. This can be done by dropping a test crate under similar conditions and measuring the time and distance it takes to reach the target. Another method is to use simulation software that can accurately model the physics of the scenario and provide a visual representation of the crate's trajectory. Additionally, double-checking the calculations and ensuring all variables are accounted for can help validate the accuracy of the results.

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