How can I find the initial speed using SUVAT equations?

[Simon143]

I am currently doing a project involving an object sliding down a slope and falling freely for a given height afterwards. The horizontal distance is recorded, as is the angle of the slope. I have been trying to create an equation for u (the initial speed) from this data, but I haven't been able to. We are given that:

y = x(tan[theta]) - ((4.9x^2)/(u^2))(1+tan^2[theta])

y = vertical displacement (known)
x = horizontal displacement (recorded)
[theta] = slope angle (recorded)
u = initial speed (required)

This seems to be a slight variation on a few other problems I've seen on this forum, and try as I have, I haven't been able to relate that help to my situation - mainly because I have to use SUVAT.

I can't seem to arrange the equation in a suitable form to easily give 'u'. I'd be really grateful for any help you could give me.

Thanks

Simon

 

[arildno]

y = x(tan[theta]) - ((4.9x^2)/(u^2))(1+tan^2[theta])

Can't you write:

u^(2)=(4.9x^2)*(1+tan^2[theta])/(x(tan[theta])-y)?

What's SUVAT by the way?

 

[Parth Dave]

y = x(tan[theta]) - ((4.9x^2)/(u^2))(1+tan^2[theta])

((4.9x^2)/(u^2))(1+tan^2[theta]) = x(tan[theta]) - y

(4.9x^2)(1+tan^2[theta]) = (x(tan[theta]) - y)(u^2)

(u^2) = (4.9x^2)(1+tan^2[theta]) / (x(tan[theta]) - y)