River flowing down a mountain

Question

A river flowing from a mountain of height 500m and the mountain makes an angle 45 degrees with the plains. The river flows along a straight path making an angle 45 degrees with the face of the mountain. Then the time taken for water to flow from top to the base is?
a) 200s
b) 14.14sec
c) 100s
d) None

Solution

If we are able to visualize the question, this one should not be very difficult.

Firstly we need to find the length of the river, which is given as follows:

So the distance travelled will be 1000m.

Now we need to find the acceleration of the water down the mountain.

The component of the acceleration down the plane is !!gsin45=g/sqrt(2)!!

But the river is flowing at !!45^@!! to the face of the plane, so it will not accelerate at !!g/sqrt(2) * sin45=g/2=5ms^-2!!

So the time taken to cover the path is !!t=sqrt(2h/g)=sqrt(2*1000/5)=20s!!

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