-
Notifications
You must be signed in to change notification settings - Fork 1
/
388f5b5f-d4c2-49c1-9311-467579b27f5e.html
71 lines (71 loc) · 3.23 KB
/
388f5b5f-d4c2-49c1-9311-467579b27f5e.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
<h3><span>Activity</span><br></h3>
<p>A rock is dropped from the top floor of a 500-foot-tall building. A camera captures the distance the rock traveled, in feet, after each second.</p>
<p><img alt="An image of a rock dropped from the top floor of a 500-foot tall building." height="474" src="https://k12.openstax.org/contents/raise/resources/1c75917d2332c9659b27a695c1adde78d6e7038e" width="377"></p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="e98a536d-c3b4-458e-a37f-a3e0da467bf3" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>How many feet will the rock have fallen after 6 seconds? Be prepared to show your reasoning.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>The rock will have fallen 500 feet after 6 seconds. The distance fallen increased with each additional second. The rock fell 144 feet between 4 and 5 seconds, so between 5 - 6 seconds, it would fall more than 144 feet. After 5 seconds of falling, there is less than 144 feet to go before the rock hits the ground.</p>
</div>
</div>
<!--Interaction End -->
<br>
<ol class="os-raise-noindent" start="2">
<li>Jada noticed that the distances fallen are all multiples of 16.<br>
<br>
She wrote down:<br>
<br>
\(16=16 \cdot 1\)<br>
\(64=16 \cdot 4\)<br>
\(144=16 \cdot 9\)<br>
\(256=16 \cdot 16\)<br>
\(400=16 \cdot 25\)
</li>
</ol>
<p>Then, she noticed that 1, 4, 9, 16, and 25 are \(1^2\), \(2^2\), \(3^2\), \(4^2\), \(5^2\).</p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="672d8c4a-91cf-45f7-8d3c-93e5f51c5180" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" type="a">
<li> Use Jada’s observations to predict the distance fallen in feet after 7 seconds. (Assume the building is tall enough that an object dropped from the top of it will continue falling for at least 7 seconds.) Be prepared to explain your reasoning.</li>
</ol>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>784</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> Write an equation for the function, with \(d\) representing the distance dropped after \(t\) seconds. </li>
</ol>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answer:</p>
<p>\(d=16 \cdot t^2\)</p>
</div>