A boy throws a ball into the air at 10.2 m/s. Assuming that only gravity acts on the ball, how high does it rise, in m?

1 answer:

ozzi3 years ago

5 0

Answer: 5.31 meters

Explanation: Use conservation of energy. Initial energy equals final energy. Initially, there is only kinetic energy (because height = 0 initially). At the end, kinetic energy equals 0 because at max height, there is max potential energy and the ball stops moving for a split second.

mgh = .5mv^2
Masses cancel out
gh = .5v^2
(9.8)(h) = .5(10.2^2)
Solve for h. h = 5.31 meters

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How do you find the speed of an object given its mass and kinetic energy (what is the formula)?

madam [21]

v = √ { 2*(KE) ] / m } ;

Now, plug in the known values for "KE" ["kinetic energy"] and "m" ["mass"] ;

and solve for "v".
______________________________________________________
Explanation:
_____________________________________________________
The formula is: KE = (½) * (m) * (v²) ;
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"Kinetic energy" = (½) * (mass) * (velocity , "squared")
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Note: Velocity is similar to speed, in that velocity means "speed and direction"; however, if you "square" a negative number, you will get a "positive"; since:  a "negative" multiplied by a "negative" equals a "positive".
____________________________________________
So, we have the formula:
___________________________________
KE = (½) * (m) * (v²) ; to solve for "(v)" ; velocity, which is very similar to the "speed";
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we arrange the formula ;
__________________________________________________
(KE) = (½) * (m) * (v²) ;  ↔ (½)*(m)* (v²) = (KE) ;
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→ We have: (½)*(m)* (v²) = (KE) ; we isolate, "m" (mass) on one side of the equation:
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→ We divide each side of the equation by: "[(½)* (m)]" ;
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→ [ (½)*(m)*(v²) ] /  [(½)* (m)] = (KE) / [(½)* (m)]<span> ;
</span>______________________________________________________
to get:
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→ v² =   (KE) / [(½)* (m)]

→ v² = 2 KE / m
_______________________________________________________
Take the "square root" of each side of the equation ;
_______________________________________________________
  → √ (v²) = √ { 2*(KE) ] / m }
________________________________________________________

→ v = √ { 2*(KE) ] / m } ;

Now, plug in the known values for "KE" ["kinetic energy"] and "m" ["mass"];

and solve for "v".
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How many times should the power develop by the engine of a ship increases to double is velocity i the resistance of the water to

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Answer:

If the ship speed is doubled, then the power developed is 8 times the initial value.

Explanation:

ship power is roughly proportional to the cube of the speed, so

P ∝ v³

If the speed is doubled, then the power developed becomes

P ∝ (2)³ = 8 times

Therefore, if the ship speed is doubled, then the power developed is 8 times the initial value.

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