Projectile Motion: An Arrow Shot & Landed at Different Points

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Homework Help Overview

The problem involves projectile motion, specifically analyzing the trajectory of an arrow shot at an initial velocity of 45 m/s at an angle of 52 degrees above the horizontal. The arrow is launched from a height of 1.5 m and lands on a roof that is 5 m high. The discussion includes questions about the arrow's ability to clear a 50 m high tree located 75 m away, its total time of flight, and the horizontal distance to the house.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the calculation of maximum height and time of flight, with one participant expressing uncertainty about how to determine horizontal displacement from a height of 1.5 m. Questions are raised about the effect of starting height on horizontal displacement and the implications of changing the ground level.

Discussion Status

Some participants have provided calculations for maximum height and time of flight, while others are exploring the implications of the starting height on horizontal displacement. There is an ongoing examination of how to approach the problem of adjusting for the initial height in calculations.

Contextual Notes

Participants are considering the effects of the initial height of the arrow on its trajectory and displacement, as well as the implications of shifting the origin of the coordinate system for calculations.

Marvels
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Homework Statement



An Arrow is shot from an initial velocity of 45 m/s 52 degrees above the horizontal. It lands on a 5 m high roof of a house. The arrow is shot from a height of 1.5 m.

(v) Would it be able to pass over a 50 m high tree located 75 m away?
(vi) What is its' total time of flight?
(vii) How far away is the house?

Homework Equations



d = vit +1/2at^2
v=d/t
a = vf-vi/t

The Attempt at a Solution



I've calculated the max height of the arrow; 65.43 m, and the time, 3.6 s.

I don't know how to calculate the horizontal displacement of an object starting 1.5 m off the ground.
 
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Marvels said:

Homework Statement



An Arrow is shot from an initial velocity of 45 m/s 52 degrees above the horizontal. It lands on a 5 m high roof of a house. The arrow is shot from a height of 1.5 m.

(v) Would it be able to pass over a 50 m high tree located 75 m away?
(vi) What is its' total time of flight?
(vii) How far away is the house?

Homework Equations



d = vit +1/2at^2
v=d/t
a = vf-vi/t

The Attempt at a Solution



I've calculated the max height of the arrow; 65.43 m, and the time, 3.6 s.

I don't know how to calculate the horizontal displacement of an object starting 1.5 m off the ground.

How does the starting height affect the horizontal displacement? What would happen to the arrow if you moved the ground up 1.5 m?
 
SteamKing said:
How does the starting height affect the horizontal displacement? What would happen to the arrow if you moved the ground up 1.5 m?

Do I add 1.5 m to the regular displacement? (Do I do the same with y disp, too?)
 
Marvels said:
Do I add 1.5 m to the regular displacement?
No, why do you think that might be valid? Please don't make wild guesses.
What you can do is make shift of origin, provided you do it consistently. I.e. add or subtract a number from all horizontal coordinates, and likewise (but maybe a different number) from all heights.
 

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