How would you proove this: vx=xsqart(g/2y) using this kinematic equation: 1/2at^2+vt+x in both the x and y directions? (I'll retype it using the equations menu)

Question

anonymous · Answer

I can't seem to get the equation to come out using the equations menu but its one of the kinematic equations for an object in projectile motion, the one with the 1/2at^2 in it.

unklerhaukus · Answer

$$a=\ddot x =\frac{\text{d}^2x}{\text{d}t^2}=g$$ integrate with respect to time
$$v=\dot x =\frac{\text{d}x}{\text{d}t}=gt$$again integrate with respect to time
$$x={gt^2\over 2}$$

unklerhaukus · Answer

$$t=\sqrt{\frac{2x}{g}}$$

unklerhaukus · Answer

i havent answered your question

anonymous · Answer

for some reason I can't see your code, it says math processing error. I'll try another internet browser to see if i'm having smilar issues there.

unklerhaukus · Answer

also  note that i assumed acceleration due to gravity as the only force acting on your projectile and that your projectile was initially stationary

unklerhaukus · Answer

attachment

anonymous · Answer

okay that works better but the answer I'm trying to proove is actually: vx(initial velocity)=x[squarert(g/2y)]

unklerhaukus · Answer

of you mean $$v_x$$

unklerhaukus · Answer

you wish to prove this$$v_x=x\sqrt{ \small \frac{g}{2y}}$$

anonymous · Answer

I can't see the equation

unklerhaukus · Answer

makes things difficult

anonymous · Answer

Sometimes when I refresh my page I can see it for a brief moment, then it goes away and shows the "math processing error" message. But from what you have shown me it looks correct.