What Is the Optimal Launch Angle for Maximum Range When Landing 3 Meters Lower?

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Homework Help Overview

The discussion revolves around determining the optimal launch angle for a projectile that is thrown from a height of 3 meters and lands 3 meters lower. Participants are exploring the physics of projectile motion, particularly how the launch angle affects the range when the landing height differs from the launch height.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to formulate equations that relate the launch angle to the range of the projectile, considering the initial velocity and the height difference. Questions arise about the correct setup of the equations and the application of differentiation to maximize the range.

Discussion Status

There is an ongoing exploration of the problem with participants sharing their attempts at formulating the equations. Some guidance has been offered regarding the use of simultaneous equations for horizontal and vertical motion, but there is no explicit consensus on the approach or solution yet.

Contextual Notes

Participants are clarifying the specifics of the problem setup, including the initial height and the landing height. There is a focus on understanding how these factors influence the launch angle needed for maximum range.

larryboi7
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How can i find the angle of which an object will be thrown the farthest?

I know the angle will be 45 degrees if it were to be catched at the same height it were thrown, but what I'm looking for is the angle if it were 3meters off the ground.

Thank you for the help.
 
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larryboi7 said:
How can i find the angle of which an object will be thrown the farthest?

I know the angle will be 45 degrees if it were to be catched at the same height it were thrown, but what I'm looking for is the angle if it were 2meters off the ground.

Thank you for the help.

Welcome to the PF. Are you familiar with how to maximize a function using differentiation? Write an equation for the range as a function of launch angle (given your offset y information). Show us your attempt at a solution so we can help.
 
berkeman said:
Welcome to the PF. Are you familiar with how to maximize a function using differentiation? Write an equation for the range as a function of launch angle (given your offset y information). Show us your attempt at a solution so we can help.

The equation would be

initial velocity is 5m/s

0 = 3 + 5sin(x) - (1/2)gt^2

x(t) = 5cos(x) * t

I know what differentiation is but I can't see how it will work to find the angle for maximum range.
 
larryboi7 said:
The equation would be

initial velocity is 5m/s

0 = 3 + 5sin(x) - (1/2)gt^2

x(t) = 5cos(x) * t

I know what differentiation is but I can't see how it will work to find the angle for maximum range.

I'm not understanding what you wrote, but it sounds like you can figure this out. BTW, is it thrown at 0m and caught at 2m, or the other way around?

I think you will write two equations (this is the usual way to solve this type of question): One for the horizontal motion, which has a constant velocitty. The other is the vertical motion equation, which involves the vertical pull of gravity. You will use them as simultaneous equations, and solve them for the final simultaneous (x,y) point. Does that help? Show us your work...
 
berkeman said:
I'm not understanding what you wrote, but it sounds like you can figure this out. BTW, is it thrown at 0m and caught at 2m, or the other way around?

I think you will write two equations (this is the usual way to solve this type of question): One for the horizontal motion, which has a constant velocitty. The other is the vertical motion equation, which involves the vertical pull of gravity. You will use them as simultaneous equations, and solve them for the final simultaneous (x,y) point. Does that help? Show us your work...

it is thrown at 3m and and caught at 0 meters.
i have the equations as stated before. would you mind showing me?
 

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