What is the relation of sinθ and time in projectile motion with angle

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Homework Help Overview

The discussion revolves around the relationship between the sine of the angle of projection (sinθ) and the time of flight in projectile motion, specifically under the condition of constant initial velocity. Participants are exploring whether this relationship can be graphed and what shape that graph would take.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to establish a proportional relationship between sinθ and time of flight, questioning if this relationship changes when the angle exceeds 45 degrees. Other participants suggest plotting time of flight against angle and propose that the graph would resemble a sine curve rather than a parabola.

Discussion Status

Some participants have provided insights into the nature of the graph, noting its similarity to a sine curve and clarifying that the relationship does not change at 45 degrees. However, there is an ongoing inquiry into the underlying reasons for this relationship and its implications.

Contextual Notes

Participants are working within the framework of projectile motion equations and are considering the implications of varying angles on time of flight, with specific attention to the behavior of the sine function in this context.

xunok123
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Homework Statement


I am wondering what is the relation of sinθ & time of flight in projectile motion with angle.
(under the case of same velocity)
Is the graph of this in a parabola shape??

Homework Equations


t = (2u sinθ) / g
(u in constant)

The Attempt at a Solution


would it be correct that sinθ ∝ time of flight ?

would the relation be affected after the angle of projection is lager than 45?

:cry: This puzzles me a lot...~_~
 
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xunok123 said:

Homework Statement


I am wondering what is the relation of sinθ & time of flight in projectile motion with angle.
(under the case of same velocity)
Is the graph of this in a parabola shape??

Homework Equations


t = (2u sinθ) / g
(u in constant)

The Attempt at a Solution


would it be correct that sinθ ∝ time of flight ?

would the relation be affected after the angle of projection is lager than 45?
Welcome to PF!

If you want to plot time of flight vs. angle I would put θ on the x-axis and t on the y axis. The graph would be a sine curve, not a parabola. It is similar in appearance to a parabola, though. There is no change in the relation at θ=45° .

The range of θ is 0 → π (180°) and reaches a maximum at θ = π/2 (90°).

AM
 
Andrew Mason said:
Welcome to PF!

If you want to plot time of flight vs. angle I would put θ on the x-axis and t on the y axis. The graph would be a sine curve, not a parabola. It is similar in appearance to a parabola, though. There is no change in the relation at θ=45° .

The range of θ is 0 → π (180°) and reaches a maximum at θ = π/2 (90°).

AM

HI Manson! Thank you so much for your answer@@! It's a big surprise for me!
would u mind have a little more explanation on this phenomenon??
I find it so interesting that the graph would appear as a sine curve.
 
Last edited:
xunok123 said:
HI Manson! Thank you so much for your answer@@! It's a big surprise for me!
would u mind have a little more explanation on this phenomenon??
I find it so interesting that the graph would appears as a sine curve.

Why does it surprise you so much when you have an equation right in your original post that says t = (some stuff)*sin(theta) ?

Andrew Mason: didn't the OP want the relation between t and sin(theta), not the relation between t and theta? The former would be linear.
 

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