You decide to get into a pool by going down the magic frictionless water slide. If the starting height of the slide is 7.8 m above the pool water’s surface, what is your speed, in m/s, upon entering the pool if your mass is 57.2 kg and you start with an initial speed of 0.8 m/s?
V^2 = Vo^2 + 2g*h. Vo = 0.8 m/s, g = 9.8 m/s^2, h = 7.8 m, V = ?.
To determine the speed at which you enter the pool, we need to use the principle of conservation of energy.
The potential energy at the top of the slide is given by:
PE = mgh
Where:
m = mass (57.2 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of the slide (7.8 m)
The initial potential energy is converted into kinetic energy as you slide down the slide. The kinetic energy can be calculated using the formula:
KE = (1/2)mv^2
Where:
m = mass (57.2 kg)
v = velocity/speed (unknown)
Since the slide is frictionless, we can assume that the total mechanical energy (potential energy + kinetic energy) remains constant throughout the slide. Therefore, the initial potential energy is equal to the final kinetic energy.
Set the two equations equal to each other:
mgh = (1/2)mv^2
Cancel the mass (m) on both sides of the equation:
gh = (1/2)v^2
Now, substitute the known values:
(9.8 m/s^2)(7.8 m) = (1/2)v^2
Simplify the equation:
76.44 = (1/2)v^2
Multiply both sides of the equation by 2:
152.88 = v^2
Take the square root of both sides to find the velocity:
v = √152.88
Using a calculator, the approximate velocity is:
v ≈ 12.36 m/s
Therefore, your speed upon entering the pool is approximately 12.36 m/s.