Abigail and Benji are tossing a ball underhand back and forth in the gym. They are standing 15 feet apart. It takes 3.5 seconds for the ball to go from one participant to the other. They play like this for 5 minutes.
1. Assign a variable to represent the height of the ball from the ground and the time it takes for a single toss. Y – Height X- Time
A. Is there a functional relationship between the height of the ball from the ground and time for a single toss? Yes, the higher the ball goes, the longer the ball is in the air for.
B. Which variable would be the independent variable? Dependent? Height would be dependent and the time would be for independent.
2. Sketch a possible graph of one toss.
A. What would be a reasonable domain and range for this single toss? Explain how you determined the possible values for the range. R- 3, 6, 3 D- 0.0, 1.75, 3.5 There’s a staring point (3ft.) then eventually the ball has its peak (6ft.), then the ball is caught at the stopping point (3ft.)
B. What would it mean if (0, 0) were a point on the graph that someone drew for this situation? It would be the resting point, 0 distance and 0 time has occurred.
C. Suppose 0 was in the range. What would that mean? No height, meaning the ball hasn’t even been picked up to toss.
D. Suppose that y = 0 represents ground level and x = 0 when the ball is first thrown. Does this match the graph that you drew? If not, explain how this changes the positioning of the axes on the graph that you drew. Yes it does match; my X represents the time while the Y represents the level of the height of the ball when thrown.
3. Sketch a possible graph for three tosses of the ball.
A. Is there a functional relationship between the height of the ball from the ground and time over three tosses of the ball? Yes, higher the ball, longer the amount of time the ball is in the air (overall time)
B. Describe the domain and range for three tosses of the ball.
D- 3, 6, 3, 6, 3, 6, 3 R- 0.0, 1.75, 3.5, 5.25, 7.0, 8.75, 10.5
4. Is the height of the ball above the ground a function of its distance from Abigail for a single toss? Explain your reasoning. Yes. If the ball needs to be thrown higher, that means there is a great distance so the ball doesn’t free fall as quickly as a more less of an arch of the ball.
A. If distance from Abigail is the independent variable; sketch a possible graph for one toss.
B. What would be a reasonable domain and range?
D- 0, 7.5, 15 R- 3. 11, 3
5. Is the height of the ball above the ground a function of the distance from Abigail for three tosses if each time the two players do not toss the ball exactly the same way? Explain. It can be, depending on the type of throw.
Option 1: Depending on the velocity of the ball when it’s thrown. One person could have a mild velocity when tosses, but a good height so it may travel the distance as compared to a line drive with a mild toss, which would result in the ball not making it from Point A to Point B.
Option 2: You could have the person toss it as fast as the can just straight upward, but not making a good amount of distance because the slope of the ball is too steep going up, and knowing it’s at a constant speed, it will have a constant slope on the way back down towards the ground/person.
Option 3: That person could just toss a straight line drive, and depending on the velocity, it might make it or not. The…