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

[xunok123]

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?

This puzzles me a lot...~_~

 

[Andrew Mason]

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

 

[xunok123]

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.

 

[cepheid]

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.

 

[Nickie]

The relation between sinθ and time in projectile motion is an inverse one, meaning that as the angle (θ) increases, the time of flight decreases. This can be seen in the equation t = (2u sinθ) / g, where u is the initial velocity and g is the acceleration due to gravity. As sinθ increases, the value of t decreases.

The graph of this relation would indeed be in a parabolic shape, as the motion of a projectile follows a parabolic path. The maximum height of the projectile would be reached at the vertex of the parabola, where the angle would be 90 degrees (sin90 = 1).

The relation between sinθ and time would still hold true for angles greater than 45 degrees, but the maximum height and range of the projectile would be affected. As the angle increases, the range of the projectile would decrease while the maximum height would increase. This is because a larger angle would result in a more vertical trajectory, leading to a shorter range but a higher maximum height.

I hope this helps clarify the relation between sinθ and time in projectile motion. Keep in mind that this is a simplified explanation and there are other factors that can affect the motion of a projectile, such as air resistance and the shape of the object.