Solve Projectile Angle Homework: Range 7x Height, Flat Landscape

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Homework Help Overview

The problem involves determining the launch angle of a projectile given that its range is seven times its maximum height, with the assumption of a flat landscape. The context is rooted in projectile motion and the equations governing the trajectory.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the nature of the projectile's trajectory and the governing equations for motion in both X and Y directions. Some express confusion over the lack of additional information, while others suggest working with symbolic representations rather than numerical values to derive relationships between the components of motion.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some guidance has been offered regarding the relationship between the components of initial velocity and the required height-range ratio, but no consensus has been reached on a specific approach or solution.

Contextual Notes

Participants note the absence of time-related information, which complicates the analysis of the projectile's motion. The assumption that the projectile is influenced by gravity near the Earth's surface is also highlighted as a necessary condition for the problem.

hechen
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Homework Statement


This is all that is given:
If the range of a projectile's trajectory is seven times larger than the height of the trajectory, then what was the angle of launch with respect to the horizontal? (Assume a flat and horizontal landscape.)

Homework Equations



X = 7y

Y= Y

Arctan (Y/X)

The Attempt at a Solution



Arctan (1/7) ~ 8.13 deg

This answer was wrong according homework website I'm using
 
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The projectile's trajectory is not a straight line. What shape is it? What equations govern the motion in the X and Y directions?
 
There were no more information given then what I posted. Which is puzzling.
 
hechen said:
There were no more information given then what I posted. Which is puzzling.

The only additional information required is the assumption that the projectile is moving under the influence of gravity near the Earth's surface. So acceleration is g in the vertical (Y) direction.
 
I would then need to know time or was way to figure out time which is not possible in this case.
"If the range of a projectile's trajectory is seven times larger than the height of the trajectory, then what was the angle of launch with respect to the horizontal? (Assume a flat and horizontal landscape.)"
If the movement here is not linear the angle of the projectile depends on time.
 
You can work with symbols rather than numbers. You're given a ratio of two distances that occur at specific times in a projectile's lifetime (max height and range), and you should be able to derive expressions for each. Also, the only angle you're interested in is the one that occurs at the instant of launch.

I'll give you a hint. The launch angle is related to the x and y components of the initial velocity. If you assume that the components are vx and vy, then the angle is atan(vy/vx). So what you're aiming for is the relationship between vx and vy in order to satisfy the height-range requirement. I'd suggest finding expressions for the maximum height and the range as functions of vx and vy.
 

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