Question

Suppose the water at the top of Niagara Falls has a horizontal speed of 1.20 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 47.3 ° angle below the horizontal?

Answer 1

Initial horizontal speed, ....................(1)

Initial vertical speed, ....................(2)

Now we need to find the vertical distance when the velocity vector of the water points below the horizontal. Let the speed at this position be "v".

Then horizontal component of the velocity at that point wil be .........(3)

And, vertical component of the velocity at that point wil be (Assuming downward direction to be positive).........................(4)

Acceleration acting horizontally,

Acceleration acting vertically,

Then since no acceleration acts on horizontal direction thus its horizontal velocity will remain same, thus we can write

  

Using equation 1 and 3,

  

Then vertical component of the velocity at the required position will be(using equation 4)

   (positive sign denotes that this velocity component is directed downwards)

Now let the distance covered below the edge be "h", then using equations of motions

  

Using equation 2 and deduced values,

  

(ANS)