ShmoopTube

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And here's your shmoop du jour...

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

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

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

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

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And here are the potential answers…

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

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

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

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

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

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

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

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

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

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the parabola is above the line.

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

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Since the question asks us for the answer approximately,

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

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

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the line between the two is roughly thirty feet.

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

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

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one second on its way up…

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

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

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but probably less than a second and a half.

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

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As in, “Boink!”

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