Question

I need an equation for finding the veocity of water at the end of an incline.

• the velocity at the top is 0
• the incline is a right triangle with a hieght of 3000ft and a base of 9 miles
• the fluid is water
• the depth of the water is 3ft

Answer 1

We know about slopes from skiing downhill in the winter or bicycling down an incline. In physics, any slopes and wedges are called inclined planes. According to Newton's law of motion, an unbalanced object kept on a frictionless inclined plane slides down the slope. The "frictionless" plane means that the plane applies no forces to the object moving down it.

Instructions-

1. Calculation Instructions-

   • 1

     Obtain measurement of the vertical height (h) of the inclined plane. Measure the distance from the bottom of the inclined plane to the top where your object starts moving. Make sure all your measurements are in the same standard unit. Know that 1 inch = 0.0254 meters.

   • 2

     Apply the principle of conservation of mechanical energy to find velocity. At the bottom of the incline plane, gravitational potential energy of the object, m*g*h, is converted into kinetic energy, 1/2*m*v^2. Write it down as: m*g*h = 1/2*m*v^2
     Arrange the equation to solve for velocity.
     V=square root(2*g*h)
     Note that the motion is frictionless and the object's kinetic energy equals zero at the top of the inclined plane.

3

• Substitute the g--acceleration due to gravity--with 9.8 meters/second^2 (constant) and h (in meters) into the formula above to find final velocity (in meters per second) of the object at the bottom of the inclined plane.

• 4

  Include in your equation the values of the angle (Q) and length (d) of the inclined plane when they are known. Calculate the final velocity of a block sliding down a 45-degree inclined plane if the length of the incline is 3 meters. Use the formula for velocity from Step 2: V=square root (2*g*h).
  Remember equations for an inclined plane (or right triangles): sin(Q) = h/d, so h = d*sin(Q). Substitute h into the velocity formula above
  V=square root(2*g*d*sin(Q)).
  Use a scientific calculator to find V=square root(2*9.8 m/s^2*3*sin(45 degrees))=6.45 m/s. This is your answer. At the bottom of the inclined plane, the block has final velocity of 6.45 meters per second.

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