The maximum velocity of a roller coaster depends on the vertical drop from the top of the highest hill to the bottom of that hill. The formula:V(h)=√h-2 , gives the relationship between maximum velocity, V(h) in feet per second, and height, h in feet.
1. Identity the independent variable, dependent variable.
2. What is the domain of the radical function V?
3. What is the maximum velocity V(h) of the roller coaster when the height h is 66 feet? (Specify and explain your answer in words.
4. What is the height h of the roller coaster, if its maximum velocity V(h) is 32 feet per second? Specify and explain your answer in words.
assuming you mean √(h-2), then the domain is [2,∞)
what's to explain? plug h=66 into the formula
v = √(66-2) = √64 = 8
√(h-2) = 32
h-2 = 1024
h = 1026
The maximum velocity of a roller coaster using the formula v=8 ^h when the height is 203 feet
1. The independent variable is the height, h in feet.
The dependent variable is the maximum velocity, V(h) in feet per second.
2. The domain of the radical function V is the set of all non-negative real numbers, since the radical function requires the input inside the square root to be non-negative. Therefore, the domain of V(h) is all values of h greater than or equal to 2.
3. To find the maximum velocity V(h) when the height h is 66 feet, substitute h = 66 into the formula:
V(h) = √(h - 2)
V(66) = √(66 - 2)
V(66) = √(64)
V(66) = 8 feet per second
When the height of the roller coaster is 66 feet, its maximum velocity is 8 feet per second.
4. To find the height h of the roller coaster when its maximum velocity V(h) is 32 feet per second, solve the formula for h:
V(h) = √(h - 2)
32 = √(h - 2)
(32)^2 = h - 2
1024 = h - 2
h = 1024 + 2
h = 1026 feet
When the maximum velocity of the roller coaster is 32 feet per second, the height of the roller coaster is 1026 feet.
1. The independent variable is the height of the roller coaster, h, in feet. The dependent variable is the maximum velocity, V(h), in feet per second.
2. The domain of the radical function V is the set of all non-negative values of h. In other words, the height cannot be negative because it represents the vertical drop of the roller coaster.
3. To find the maximum velocity V(h) when the height h is 66 feet, we can substitute 66 into the formula V(h) = √h-2.
V(66) = √(66) - 2
V(66) = √64
V(66) = 8 feet per second
Therefore, the maximum velocity of the roller coaster when the height is 66 feet is 8 feet per second. This means that at the bottom of the hill, the roller coaster will be moving at a speed of 8 feet per second.
4. To find the height h of the roller coaster when its maximum velocity V(h) is 32 feet per second, we can rearrange the formula V(h) = √h-2 and solve for h.
32 = √h - 2
To remove the square root, we square both sides of the equation:
(32)^2 = (√h - 2)^2
1024 = h - 4
Now, we can isolate h by adding 4 to both sides of the equation:
h = 1024 + 4
h = 1028 feet
Therefore, the height of the roller coaster when its maximum velocity is 32 feet per second is 1028 feet. This means that the roller coaster must have a vertical drop of 1028 feet from the top of the highest hill to the bottom of that hill.