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Consult Multiple-Concept Example 4 for background before beginning this problem. Suppose the water at the top of Niagara Falls has a horizontal speed of 2.7 m/s just before it cascades over the edge of thefalls. At what vertical distance below the edge does the velocity vector of the water point downward at a 75 angle below the horizontal?

$h=5.18 \mathrm{m}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

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So the question states that water fall flows off a waterfall at 2.7 meters per second in the horizontal direction, and we're trying to find at what height below starting point was call it X. Will the Voss defector be at a 75 degree angle from the horizontal? So we know that the horizontal velocity will always be constant because its projectile motion So this will the horizontal component will be 2.7 meters per second. We don't know what the vertical component is, but we do know that the angle here will be 75 degrees. Knowing this, we can figure out what d uh total magnitude of the lost he is. So we know that CO sign of 75 degrees is equal to at the adjacent overhype oddness. In this case 2.7 over V and we can sell for V and we'll find that V is equal to 10 point 431 meters per second. Now that we know what V is we can solve for V of why? Because we know that sign of 75 degrees is equal to the of why over the opposite over high Panis and we know what V is from here. So we find that V of Y is equal to 10.8 meters per second. Now that we know what the vertical velocity is to get the water toe, be an angle at 75 degrees the velocity to be an angle of 75 degrees. We can use our kinetics formula which state that the velocity at Time T square is equal to the initial velocity squared plus two times the acceleration, times, change and displacement. So we know that our final vertical velocity is going to be 10.8 meters per second squared that we know the initial vertical velocity is going to be zero because the water is coming off horizontally from the waterfall and we know our acceleration is going to be 9.8 meters per second squared. This acceleration is in the same direction as this velocity. That's why signs of the same and we are trying to find what X is equal to. So when we saw for this we find out that the displacement is going to be five point 18 meters

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