- #1

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Hi,

I think it is atan of the derivative of the curve, is that right?

Thanks

Matt

I think it is atan of the derivative of the curve, is that right?

Thanks

Matt

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- Thread starter Matt Jacques
- Start date

- #1

- 81

- 0

Hi,

I think it is atan of the derivative of the curve, is that right?

Thanks

Matt

I think it is atan of the derivative of the curve, is that right?

Thanks

Matt

- #2

mathman

Science Advisor

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- #3

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Thanks for the quick reply. Yeah, that is what I thought. However, I have a followup question.

For the vertical position of a projectile the formula is:

y = initialheight + VyT - .5(9.8)T^2

The derivative of that is

d/dx = Vy - 9.8T

I did a sample problem, Vi=4, angle = 30º, initial height = 1.2

Total Time: .739 seconds

Height of Max time: .202 seconds

Distance: 2.56 m

if I take atan( Vy - 9.8T) when t = 0 the angle comes up as 63º, not 30º which it should be.

Hmm?

For the vertical position of a projectile the formula is:

y = initialheight + VyT - .5(9.8)T^2

The derivative of that is

d/dx = Vy - 9.8T

I did a sample problem, Vi=4, angle = 30º, initial height = 1.2

Total Time: .739 seconds

Height of Max time: .202 seconds

Distance: 2.56 m

if I take atan( Vy - 9.8T) when t = 0 the angle comes up as 63º, not 30º which it should be.

Hmm?

Last edited:

- #4

- 136

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I started to work out the problem, but you didn't state it quite clearly....

Do you mean V_{0x} is the initial Vi in the direction of **vector i** ?

Do you mean V

Last edited:

- #5

HallsofIvy

Science Advisor

Homework Helper

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dy/dt has no geometric meaning (in an xy-coordinate system).

If Vi= 4 is the initial speed and the projectile is fired at a 30 degree angle to the horizontal, then the initial vertical speed is Vy= 4 cos(30)= 4(1/2)= 2 and the initial horizontal speed is

Vx= 4 sin(30)= 4([sqrt](3)/2)= 2 [sqrt](3).

The vertical speed would be given by dy/dt= 2- 9.8t and the horizontal speed (assuming gravity is the only force) by

dx/dt= 2[sqrt]3. At t= 0, dy/dt= 2 and dx/dt= 2[sqrt](3).

By the chain rule, dy/dx= (dy/dt)/(dx/dt)= 2/2[sqrt](3)= 1/[sqrt](3)= [sqrt](3)/3, the tangent of 30 degrees.

- #6

- 81

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Thanks, Hallsofivy. You created a good thorough reply. However, I think you accidentally swapped cosine and sine in Vx and Vy.

Anyway, for the benifit of searches, here is the formula for the angle:

http://homepage.mac.com/jjacques2/angle.gif [Broken]

Anyway, for the benifit of searches, here is the formula for the angle:

http://homepage.mac.com/jjacques2/angle.gif [Broken]

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