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1 answer:
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Answer:
y=1/2x+2
Step-by-step explanation:
The equations come in the form of y=mx+c, where m is the gradient and c is the y-intercept. Looking at the graph we know that the y-intercept is (0,2), so that rules out options B and C.
To find the gradient is a little more tricky, but we can follow the formula:
, where rise is the vertical value and run is the horizontal value
So we sub in our values:
And simplify:
So now we sub in our new found values into y=mx+c:
y=1/2x+2
Answer:
(a) The time the T-shirt takes to maximum height is 2 seconds
(b) The maximum height is 68 ft
(c) The range of the function that models the height of the T-shirt over time given above is
Step-by-step explanation:
Here, we note that the general equation representing the height of the T-shirt as a function of time is
Where:
h = Height reached by T-shirt
t = Time of flight
u = Initial velocity = 64 ft/s
g = Acceleration due to gravity (negative because upward against gravity) = 32 ft/s²
h₁ = Initial height of T-shirt = 4 ft
(a) The maximum height can be found from the time to maximum height given as
v = u - gt
Where:
u = Initial velocity = 64 ft/s
v = Final upward velocity at maximum height = 0 m/s
g = 32 ft/s²
Therefore,
0 = 64 - 32·t
32·t = 64 and
t = 64/32 = 2 seconds
(b) Therefore, maximum height is then
∴ h = 68 ft
The T-shirt is then caught 41 ft above the court on its way down
(c) The range of the function that models the height of the T-shirt over time given above is derived as
With u = 64 ft/s
g = 32 ft/s² and
h₁ = 4 ft
The equation becomes
.