A child slides down a water slide of a height h. Calculate final velocity of the child?
initial PE=final KE
mg h=1/2 m v^2
solve for v
To calculate the final velocity of the child sliding down a water slide, you can use the concept of conservation of mechanical energy. The initial potential energy of the child at the top of the water slide is converted into kinetic energy at the bottom.
The potential energy at the top can be calculated using the formula: P.E. = mgh, where m is the mass of the child, g is the acceleration due to gravity, and h is the height of the water slide.
The kinetic energy at the bottom can be calculated using the formula: K.E. = 1/2 mv^2, where m is the mass of the child and v is the final velocity.
Since energy is conserved, we can equate the potential energy with the kinetic energy:
mgh = 1/2 mv^2
Simplifying the equation, we can cancel out the common factor "m":
gh = 1/2 v^2
To find the final velocity, isolate v:
v^2 = 2gh
Taking the square root of both sides:
v = √(2gh)
Therefore, the final velocity (v) of the child sliding down a water slide of height (h) is given by v = √(2gh).