Answer:
Approximately . (Assuming that the drag on this ball is negligible, and that .)
Explanation:
Assume that the drag (air friction) on this ball is negligible. Motion of this ball during the descent:
- Horizontal: no acceleration, velocity is constant (at is constant throughout the descent.)
- Vertical: constant downward acceleration at , starting at .
The horizontal velocity of this ball is constant during the descent. The horizontal distance that the ball has travelled during the descent is also given: . Combine these two quantities to find the duration of this descent:
.
In other words, the ball in this question start at a vertical velocity of , accelerated downwards at , and reached the ground after .
Apply the SUVAT equation to find the vertical displacement of this ball.
.
In other words, the ball is below where it was before the descent (hence the negative sign in front of the number.) The height of this cliff would be .
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Let's apply an equation of equilibrium to the situation: The sum of the moments about the left end of the board must equal 0.
We have three moments to add. Positive force values indicate upward direction and negative values indicate downward direction. All distances given below are measured to the right side of the left end of the board:
- The weight of the board, -125N, located at 2m (center of the board due to its uniform density)
- The tension in the right chain, +250N, located at 4m
- The weight of the person, -500N, located at a distance "x"
The sum of the moments must equal 0 and is given by:
ΣFx = 0
F is the magnitude of force, x = distance from the left end of the board
Plug in all of the force and distance values and solve for x:
ΣFx = 250(4) - 125(2) - 500x = 0
500x = 750
x = 1.5m