- #1
Whakataku
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Imagine a ramp setup on top of a tall table. The height Δy is measured. To find the initial velocity at the instant the ball leaves the ramp, I set up the kinetic energy and potential energy equal to each other to find the initial velocity of the x component.
PE = KE
m*g*(hr) = 0.5*m*v^2
where hr is the height of the ramp and v is initial velocity (x-component)
solving for vx (x-component velocity), I got:
vx = √(2*g*hr)
To get the time for the object's time in flight:
y'-y= vy + 0.5gt^2
Δy= vy + 0.5gt^2, where Δy is the height from the ground to the ramp.
since θ= 0° I found t to be:
t = √{ (2*∆y)/g }
Now my question is how do I find the range of this object?
I started out with Δx = vx*t ; where vx is the initial x-component velocity... is that even right?
I'm hesitant to use it because written as Δx/t, it looks like an average velocity equation.
Furthermore, in Wikipedia I saw the equation
d= {v*cos( )}/g * [v*sin( ) + sqrt(v*sin( )^2+2g*y)]
http://en.wikipedia.org/wiki/Range_of_a_projectile"
under uneven ground
but the problem is I don't have final velocity... or can I calculate the final velocity with the givens... if so how??
Could anyone please nudge me in the right direction to find Δx?
thanks.
PE = KE
m*g*(hr) = 0.5*m*v^2
where hr is the height of the ramp and v is initial velocity (x-component)
solving for vx (x-component velocity), I got:
vx = √(2*g*hr)
To get the time for the object's time in flight:
y'-y= vy + 0.5gt^2
Δy= vy + 0.5gt^2, where Δy is the height from the ground to the ramp.
since θ= 0° I found t to be:
t = √{ (2*∆y)/g }
Now my question is how do I find the range of this object?
I started out with Δx = vx*t ; where vx is the initial x-component velocity... is that even right?
I'm hesitant to use it because written as Δx/t, it looks like an average velocity equation.
Furthermore, in Wikipedia I saw the equation
d= {v*cos(
http://en.wikipedia.org/wiki/Range_of_a_projectile"
under uneven ground
but the problem is I don't have final velocity... or can I calculate the final velocity with the givens... if so how??
Could anyone please nudge me in the right direction to find Δx?
thanks.
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