Answers:
A. x = 8 seconds
B. y = 80 feet . We know because it is the peack of the graph.
C. x = 3 s, x=5 s
Step-by-step explanation:
To easily solve this three part problem, we use a graphing tool to plot the equation that describes the height of the tennis ball over time, after it was hit by a tennis racket. Please, see the attached graph for clarification.
y = -5x^2 + 40*x
(the equation must have the minus sign, otherwise it makes no sense for the problem)
Where,
y = height of the tennis ball in feet,
x = seconds after the ball is hit with the racket
Question A
How long does it take for the ball to hit the ground?
By examining the graph, we need to find the points where the graph intersects with the x-axis.
This is equivalent to making y = 0 in the equation and solving for x
0 = -5x^2 + 40*x
We get two solutions, but time must be positive so, x > 0
The graph shows that when x = 8 seconds, y = 0
-5(8)^2 + 40*(8) = 0
Question B
What is the highest point reached during the flight of the ball? how do you know?
By examining the graph, we need to find the point where the graph has maximum amplitude.
The point corresponds to (4,80), y = 80 feet at x = 4 seconds
We know because it is the maximum peak of the plot. Please see attached picture for reference.
Question C
When was the ball exactly 75 feet off the ground?
We look for y = 75 feet in the plot.
This corresponds to x = 3 seconds and x=5 seconds
This can also be found analytically
75 = -5x^2 + 40*x
75 = -5(3)^2 + 40*(3)
