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CAHSEE Math 4.3 Mathematical Reasoning 180 Views


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Mathematical Reasoning Drill 4, Problem 3. For approximately how long did the pie remain higher than the three-story building?

Language:
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Transcript

00:03

And here's your shmoop du jour...

00:05

The following graph shows the relationship between the height (in feet) of a cream pie that

00:09

a clown threw from the ground with an initial velocity of 48 feet per second, and the time (in seconds).

00:15

It is estimated that the height of a one-story building is 10 feet.

00:20

For approximately how long did the pie remain higher than the three-story building?

00:24

And here are the potential answers…

00:28

The question asks roughly how long the object was higher than a three-story building.

00:32

It also tells us that the height of one story is 10 feet.

00:36

We can multiply 10 by 3, since we want a three-story building,

00:40

to get that a three-story building that is thirty feet high.

00:43

So, we want to figure out how long the pie was at least thirty feet high.

00:48

To do this, we need to figure out about where thirty feet is on our graph.

00:52

The graph shows the height of the pie in terms of time, which is perfect for us, since we

00:56

want to figure out how long the object was above thirty feet.

01:01

In other words, if we draw a line at y equals thirty feet, we want to figure out how long

01:05

the parabola is above the line.

01:08

We can see that on the y-axis, 24.188 and 36.281 are marked.

01:13

Since the question asks us for the answer approximately,

01:16

we can round a little bit and consider those as 24 and 36.

01:21

Luckily for us, 30 is exactly in between 24 and 36, which means that

01:25

the line between the two is roughly thirty feet.

01:28

Now all we have to do is find where the curve has a y-value greater than thirty.

01:33

We can see that it intersects the line we’ve designated as about thirty a little before

01:37

one second on its way up…

01:39

…and it intersects the line a little past two on its way down.

01:43

This comes out to covering a distance on the x-axis that’s a little more than one second,

01:47

but probably less than a second and a half.

01:51

The only answer that fits that criterion is (B), 1.2 seconds.

01:55

As in, “Boink!”

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