Interpreting nonlinear expressions — Basic example
About this video
A function h(t) models the height in meters of a basketball t seconds after it is thrown straight up. Evaluating at t = 0 leaves only the constant 1.2, so 1.2 is the ball's initial height in meters. The video rules out maximum height, time in the air and initial speed.
You'll be able to
- interpret the constant term of a height model as the starting height.
- use h(0) and units to decide what a number in a model represents.
Key words
- initial height
- The height of an object at the start, when t = 0.
- constant term
- The number in an expression with no variable attached, like 1.2.
- units
- What a number measures, like meters for height or seconds for time.
Transcript
- [Instructor] We're told the function above models the height h, in meters, of a basketball above ground t seconds after being thrown straight up in the air. What does the number 1.2 represent in the function? So pause this video and think about it on your own before we work through it together.
All right, so we could just visualize what's happening when you throw a basketball straight up in the air. This is the ground. Let's say this is the person throwing the basketball. This is the basketball. It starts at some height. So whatever height this is, that's its initial height at t equals zero.
And then, it's gonna be thrown with some upward velocity. And it's initially going to be a high velocity, but then it's gonna slow down. And then, at some point, it's gonna be stationary, and then it's gonna start accelerating back downwards. Now, as I mentioned, at t equals zero, what do we see over here?
Well, let's see, h of zero is going to be equal to, this term goes away, 'cause anything times zero is zero. That term goes away. And we're just left with 1.2, the exact number that they're thinking about. So if you think about it, h of zero, this tells you the position of the ball, in terms of meters above the ground, right when we are starting.
So it's telling us the initial height of the ball. So let's see, it looks like that's exactly what they're saying for choice A, the initial height, in meters, of the basketball. The maximum height in meters of the basketball? No, that's definitely not saying that.
The maximum height is not going to occur at t equals zero. It's going to occur sometime after that. Rule that one out. The amount of time in seconds the basketball remains airborne. No, that's not the case. Any value that h takes on, remember, h is in meters. T, which is an input into the function, is time.
So if you're talking about something that h is equal to, which, in this case, h is equal to 1.2 and t is equal to zero, you're talking about a height above the ground. And then the initial speed. Well, once again, no, this is h of zero, which is the height above the ground.
So we like choice A.
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