A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) fro
m the ground is given by h(t) = 5 + 64t – 16t2 where t is time in seconds. Using a graphing calculator, determine at what time the ball reaches its maximum height.
2 answers:
Answer:
2 seconds
Step-by-step explanation:
Given : A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) from the ground is given by where t is time in seconds.
To Find: Using a graphing calculator, determine at what time the ball reaches its maximum height.
Solution:
Plot the graph of the given equation
Refer the attached graph
So, the given equation is a downward parabola
So, the y coordinate of vertex of the parabola will give its maximum height and x coordinate will given the time at which the ball is at maximum height
So, Vertex = (2,69)
Maximum height = 69 feet
Time to reach maximum height = 2 seconds
Hence it will take 2 seconds to reach its maximum height.
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Answer:
Aidan is 2 miles far from the ending point when he reaches the water station.
Step-by-step explanation:
The locations of the starting point, water station and ending point are (3, 1), (3, 7) and (3, 9), all expressed in miles. First we determine the distances between starting and ending points and between starting point and water station by the Pythagorean Theorem:
From starting point to ending point:
(Eq. 1)
From starting point to water station:
(Eq. 2)
The distance between the water station and the ending point is:
(Eq. 3)
Hence, Aidan is 2 miles far from the ending point when he reaches the water station.