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

AI Thread Summary
The relationship between sinθ and time of flight in projectile motion, given a constant velocity, is directly proportional, as indicated by the equation t = (2u sinθ) / g. When plotting time of flight against the angle of projection, the graph resembles a sine curve rather than a parabola, peaking at θ = 90°. The relationship remains unchanged at an angle of 45°, and the maximum time of flight occurs at 90°. The discussion highlights the importance of understanding the distinction between the relationship of time with sinθ versus the angle θ itself. This clarification emphasizes the linear nature of the relationship between time and sinθ.
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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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