Solid sphere: gh=(7/10)v^2
Hollow sphere: gh=(5/6)v^2
Solid Cylinder: gh=(3/4)v^2
Hollow Cylinder: gh=v^2
m=mass (kilograms)
g=gravity (9.8 meters per second^2)
x sin q
h=height (meters)
r=radius (meters)
v=velocity (meters per second)
Mass cancels because it remains
constant throughout the equation.
gh=(7/10)v^2
(9.8 x sin 35)(23)=(7/10) v^2
(5.621049076)(23)=(7/10) v^2
129.2841288=(7/10) v^2
(129.2841288)/(7/10)=v^2
184.6916125=v^2
(Take the square root)
v=13.59 meters/sec
2. A plastic beach ball with a mass of .5 kilograms is rolling down a sand dune at angle of 41 degrees. The sand dune is 7.5 meters above sea level. This object is a hollow sphere. Solve for the velocity of the beach ball.
gh=(5/6)v^2
(9.8 x sin 41)(7.5)=(5/6)v^2
(6.429378484)(7.5)=(5/6)v^2
48.22033863=(5/6)v^2
(48.22033863)/(5/6)=v^2
(Take the square root)
v=7.606865738 meters/sec
3. Someone carelessly left a soda can on a freeway. A massive earthquake occurs and the freeway splits in half approximately 33.2132154515142 meters from the soda can. The can begins to roll down the freeway which is at an angle of 83 degrees. The can starts at a height of exactly 252.132 meters. The can is empty, which increases the fine to exactly $1000, however its' mass is exactly .35 kilograms. The can is an empty cylinder, solve for the velocity of the soda can as it rolls down the freeway.
gh=v^2
(9.8 x sin 83)(252.132)=v^2
(9.726952286)(252.132)=v^2
2452.475934=v^2
(Take the square root)
v=49.52247908 meters/sec
This is fast enough, that if it struck a rescue worker in the head, it might cause serious injury. Then the forensics team would be able to lift the finger prints from the can and charge the owner with both littering and assault. So don't litter!
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