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CAHSEE Math 4.3 Mathematical Reasoning 180 Views
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Description:
Mathematical Reasoning Drill 4, Problem 3. For approximately how long did the pie remain higher than the three-story building?
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?
Full Transcript
- 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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