Finding Velocity of Rolling Ball

AI Thread Summary
To determine the speed at which a ball must be shot from point P to land at a distance d of 5.80 cm, the discussion emphasizes using kinematics and energy conservation principles. The vertical heights h1 and h2 are provided, with h1 at 4.80 cm and h2 at 1.60 cm, which are crucial for calculating the time it takes for the ball to fall from h2. The horizontal velocity of the ball on the plateau can be derived from the known distance d. Energy transfers between kinetic and potential forms during the ball's ascent and descent must be considered to find the initial velocity at point P. The conversation highlights the need to apply projectile motion equations to solve for the required launch velocity.
GingerBread27
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In Figure 11-36, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h1 = 4.80 cm and h2 = 1.60 cm. With what speed must the ball be shot at point P for it to land at d = 5.80 cm?

Can someone give me a push in the right direction?
 

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This is a kinematics problem. How much time would it take an object to fall from h2? Now you know d, so can you find the horizontal velocity of the ball on the plateau? Now consider the energy transfers (kinetic-potential and vice versa) that occur during the ball's travel up the slope, and you should be able to find initial velocity at P.
 
Don't get it...sigh
 
use the projectile equations to figure out the velocity you would need when the ball leaves the edge so that you would get that range.

2nd consider the energy required to make it up the ramp and also have the velocity of part one

then ur done
 
I know it deals with energy conservation but I can't remember the equation to use for projectile motion.
 
AIM me at greenman100
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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