You (70 kg) are standing at the top of a diving board (6m) about to jump in. you decided to cannonball" (tuck your arms and legs into your sides) into the water and make the biggest splash you can so you leap upward at a velocity of 3m / s what is your velocity just before you splash into the water?
a. 10.84 m/s
b. 3 m/s
c. 14.25 m/s
d. 11.25 m/s

To calculate the velocity just before splashing into the water, we can apply the principle behind the law of conservation of energy, which states that energy cannot be created nor destroyed.

This means that the total gravitational potential energy is equal to the total kinetic energy.

The formula for gravitational potential energy is given as:

U = mgh, where:

U represents gravitational potential energy
m represents the mass
g represents the acceleration due to gravity
h represents the height at which the object is held above the surface

The formula for kinetic energy is given as:

K = 0.5mv², where:

K represents kinetic energy
m represents the mass
v represents velocity

According to the law of conservation of energy, we can set these equations equal to each other, since the total gravitational potential energy must be equal to the total kinetic energy.

mgh = 0.5mv²

We can simplify this equation further by canceling out the m's, meaning that mass is irrelevant in calculating the final velocity.

gh = 0.5v²

Plugging in our given values for h = 6m and g = 9.81m/s²:

(9.81)(6) = 0.5v²

Now, let's solve for v:

v² = [tex]\frac{(9.81)(6)}{0.5}[/tex]

v.= [tex]\sqrt{\frac{(9.81)(6)}{0.5}}[/tex]

v.= 10.84

Therefore, the velocity just before splashing in the water is 10.84 m/s.

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