This question involves the concepts of the law of conservation of energy, kinetic energy, and potential energy.
The height of the hill is "166.76 m".
<h3>LAW OF CONSERVATION OF ENERGY:</h3>
According to the law of conservation of energy at the highest point of the roller coaster ride, that is, the hill, the whole (maximum) kinetic energy of the roller coaster is converted into its potential energy:

where,
- h = height of the hill = ?
= maximum velocity = 57.2 m/s
- g = acceleration due to gravity = 9.81 m/s²
Therefore,

<u>h = 166.76 m</u>
Learn more about the law of conservation of energy here:
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Answer: F(t) = 11 - 0.9(t)
Explanation:
We know the following:
The candle burns at a ratio given by:
Burning Ratio (Br) = 0.9 inches / hour
The candle is 11 inches long.
To be able to create a function that give us how much on the candle remains after turning it after a time (t). We will need to know how much of the candle have been burned after t.
Let look the following equation:
Br = Candle Inches (D) / Time for the Candle to burn (T) (1)
Where (1) is similar to the Velocity equation:
Velocity (V) = Distance (D)/Time(T)
This because is only a relation between a magnitude and time.
Let search for D on (1)
D = Br*T (2)
Where D is how much candle has been burn in a specif time
To create a function that will tell us how longer remains of the candle after be given a variable time (t) we use the total lenght minus (2):
How much candle remains? ( F(t) ) = 11 inches - Br*t
F(t) = 11 - 0.9(t)
F(t) defines the remaining length of the candle t hours after being lit
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Answer:
idk, idk cause i'm steppin on my toes and i can't stop i make flips ou of my flops
Explanation:
Answer: final Velocity v = 10.2m/s
Explanation:
Final speed v(t) is given as
v(t) = u + at .......1
Where; u = the initial speed
a = acceleration
t = time taken
The total distance travelled d is given as
d = ut + 1/2(at^2)
Given
d = 5.0m
u = 2.0m
a = g = 10m/s2 (acceleration due to gravity)
Substituting into the equation above we have
5 = 2t + 5t^2
5t^2 +2t -5 = 0
Applying the quadratic formula. We have;
t = 0.82s & t = -1.22s
t cannot be negative
t = 0.82s
From equation 1 above
v = 2.0m/s + 10(0.82)m/s
v = 10.2m/s