About this video
Katie throws a ball for her dog and a graph shows its height over time. Sal checks four statements against the graph: she did not throw it from 5 m, it did reach about 31 m, it was in the air for nearly 5 seconds rather than 2 1/2, and it peaked at about 2 1/2 seconds.
You'll be able to
- read the starting height, maximum height and landing time from a height-time graph.
- decide whether a statement about a graph is true, paying attention to words like 'about'.
- tell the difference between the time to reach the top and the total time in the air.
Key words
- y-intercept
- Where the graph meets the height axis; here, the height the ball was thrown from.
- Highest point
- The top of the parabola (its vertex), showing the maximum height.
- Model
- A function f that describes the ball's height in metres at each time in seconds.
Transcript
- [Instructor] Katie throws a ball in the air for her dog to chase. The function f models the height of the ball, in meters, as a function of time, in seconds, after Katie threw it. And we could see that right over here. This is our function f. So at time t equals zero, the height looks like it's a couple of meters.
And then as we go forward in time, to a little under 2 1/2 seconds, the ball's going up. And then after a little under 2 1/2 seconds, the ball starts going down. And after, by the time you get to five seconds or close to five seconds, it looks like the ball is on the ground.
Its height is zero meters. So then they ask us which of these statements are true? Choose all that apply. So pause this video, and see if you can work it out. All right, now let's look through the choices. So the first one says Katie threw the ball from a height of five meters.
So let's see if that bears fruit or (chuckles) see if that's true. So if she threw it from a height of five meters, that means that the y-intercept would've been at five meters. At time t equals zero, we would've been at a height of five meters. Clearly, that is not the y-intercept.
It looks like she threw it from a height of maybe 1 1/2 or two meters. So I'm assuming that Katie is not five meters tall. So she wasn't on a ladder or anything. She just threw it from her regular height. And so we can rule out this first choice. The second one says at its highest point, the ball was about 31 meters above the ground.
Let's see if that is true. So the highest point is right over here. And yeah, that looks about 31 meters, so I like that choice. So I will select that one. The ball was in the air for about 2 1/2 seconds. So we can clearly see that that is not the case. The ball was going up for about 2 1/2 seconds, but then it was going down for roughly another 2 1/2 seconds.
And so it was actually in the air for almost five seconds. So I would rule this one out. The ball reached its highest point in the air about 2 1/2 seconds after Katie threw it. So let's see, after Katie, 2 1/2 seconds after Katie threw the ball, it's right over there.
It looks like it reached its highest point a little bit before that. But they said about, so they're speaking in rough terms. So I think that statement can be true. It's about 2 1/2 seconds. If they said exactly 2 1/2 seconds, I wouldn't have selected it 'cause it seems like it happened at like 2.45 seconds or something like that.
But there you go, those are the ones that seem true.
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