We have the following equation for height:
h (t) = (1/2) * (a) * t ^ 2 + vo * t + h0
Where,
a: acceleration
vo: initial speed
h0: initial height.
The value of the acceleration is:
a = -g = -9.8 m / s ^ 2
For t = 0 we have:
h (0) = (1/2) * (a) * 0 ^ 2 + vo * 0 + h0
h (0) = h0
h0 = 0 (reference system equal to zero when the ball is hit).
For t = 5.8 we have:
h (5.8) = (1/2) * (- 9.8) * (5.8) ^ 2 + vo * (5.8) + 0
(1/2) * (- 9.8) * (5.8) ^ 2 + vo * (5.8) + 0 = 0
vo = (1/2) * (9.8) * (5.8)
vo = 28.42
Substituting values we have:
h (t) = (1/2) * (a) * t ^ 2 + vo * t + h0
h (t) = (1/2) * (- 9.8) * t ^ 2 + 28.42 * t + 0
Rewriting:
h (t) = -4.9 * t ^ 2 + 28.42 * t
The maximum height occurs when:
h '(t) = -9.8 * t + 28.42
-9.8 * t + 28.42 = 0
t = 28.42 / 9.8
t = 2.9 seconds.
Answer:
The ball was at maximum elevation when:
t = 2.9 seconds.
Answer:
The helicopter uses 35 gallons to fly for 5 hours.
Explanation:
The amount of gas that a helicopter uses for flying varies directly proportional to the number of hours spent flying.
g ∝ T
where g represents amount of gas and T time of flight.
Then,

The helicopter files 4 hours and uses 28 gallons of fuel.
Here, g₁= 28 gallons, T₁=4 hours
g₂=?, T₂=5 hours.


⇒28×5= g₂×4
⇒ g₂×4=28×5

gallons
The helicopter uses 35 gallons to fly for 5 hours.
Assumes the shape and volume of its container
<span>particles can move past one another</span>
Answer:
a)-1.014x
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b)3.296 x
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Explanation:
For Sphere A:
mass 'Ma'= 47kg
xa= 0
For sphere B:
mass 'Mb'= 110kg
xb=3.4m
a)the gravitational potential energy is given by
= -GMaMb/ d
= - 6.67 x
x 47 x 110/ 3.4 => -1.014x
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b) at d= 0.8m (3.4-2.6) and
=-1.014x
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The sum of potential and kinetic energies must be conserved as the energy is conserved.
+
=
+ 
As sphere starts from rest and sphere A is fixed at its place, therefore
is zero
=
+ 
The final potential energy is
= - GMaMb/d
Solving for '
'
=
+ GMaMb/d => -1.014x
+ 6.67 x
x 47 x 110/ 0.8
= 3.296 x
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Answer: An 8 kg book at a height of 3 m has the most gravitational potential energy.
Explanation:
Gravitational potential energy is the product of mass of object, height of object and gravitational field.
So, formula to calculate gravitational potential energy is as follows.
U = mgh
where,
m = mass of object
g = gravitational field = 
h = height of object
(A) m = 5 kg and h = 2m
Therefore, its gravitational potential energy is calculated as follows.

(B) m = 8 kg and h = 2 m
Therefore, its gravitational potential energy is calculated as follows.

(C) m = 8 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.

(D) m = 5 kg and h = 3 m
Therefore, its gravitational potential energy is calculated as follows.

Thus, we can conclude that an 8 kg book at a height of 3 m has the most gravitational potential energy.