How Long and Fast Does an Arrow Need to Travel to Clear a Tree?

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Homework Help Overview

The problem involves determining the necessary speed and time for an arrow to clear a tree that is 45 meters high, located 60 meters away from the archer. The context is projectile motion, specifically focusing on the initial conditions required for the arrow's trajectory.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the implications of the problem's wording regarding the angle of launch and the maximum height. There are suggestions to consider different angles and the relationship between horizontal and vertical motion. Some participants propose using equations of motion to set up the problem, while others mention alternative approaches like energy considerations.

Discussion Status

The discussion is ongoing, with various interpretations of the problem being explored. Some participants have offered guidance on how to set up equations based on horizontal and vertical components of motion. There is no explicit consensus on the approach, but productive suggestions have been made to clarify the problem's requirements.

Contextual Notes

Participants note that the problem may lack specific details regarding the angle of launch, which could affect the calculations. The original poster expresses a desire for guidance without direct answers, indicating a focus on self-discovery in solving the problem.

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Homework Statement


An archer wants to fire a 0.2kg arrow so that it will just clear the top of a tree. The tree is 45m high and at a horizontal distance of 60m from the archer.

Calculate the time it will take the arrow to reach the required height and the horizontal speed it takes to reach the tree in this time.


Homework Equations


I'm not too sure...?


The Attempt at a Solution


I'm looking for some guidance to point me in the right direction rather than the answer. I WANT TO WORK IT OUT MYSELF! :D
 
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Welcome to PF, kidnappin.
As it stands, there are an infinite number of correct answers!
For each angle you choose, there is a speed that will work.
Could you have missed a given angle in the question?
We could solve it for the minimum initial speed. Any more information at all in the question?
 
I don't know, Delphi, I would assume it is implying the max height is the height of the tree as well. That's how I picture "just clear a tree". So you can find an initial vertical velocity by assuming that it clears the tree with 0 vertical velocity. Then you can use that to find the time and so on.
 
Last edited:
That sounds sensible, Sethric!
In all these projectile motion problems, I like to start with two headings:
horizontal and vertical.
In the horizontal part, you have motion at constant speed so you write the formula for that, d = vt. Or x = Vx*t if you prefer.
In the vertical part, you have accelerated motion at a=g = -9.81 so a few formulas apply - usually V = Vy + at and y = Vy*t + 0.5*a*t² work very well. Here Vx and Vy are the horizontal and vertical components of the initial velocity V.

If you put in all the known numbers into the 3 equations, you will have 3 equations with three unknowns, t, Vx and Vy. Take t to be the time to maximum height, where Vy = 0, x = 60 and y = 45. Write those up and show us! After you get them right, the problem reduces to solving the system of 3 equations with 3 unknowns.
 
I would've used energy, but them again, I'm lazy.
 

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