In this activity, two-dimensional vectors (with x- and y-components) are involved in finding the resultant vector. COMPONENT METHOD will be used to add these vectors. There is a treasure buried in the land of d, = 10 km, 45 NE d, = 20 km, 90S d,= 30 km, O w Physica! And everyone can use the map to get that treasure! Jack wanted to find it first by applying his knowledge in Vector starting pont addition. Can vou help. Jack? de X+ STEP 1: Write all the given information. TREASURE! di = 10 km, 45° NE d2 = 20 km, 90° S d3 = 30 km, 0° W Figure 3. Treasure Map STEP 2: Solve for the x- and y- components. Use your scientific calculator in computation. X-component V = V cos e y-component Vy = V sin 0 Vectors STEP 3: Compute for the summation of Vx and V, dix = 10 km cos 45° dıy = 10 km sin 45° d1 EV = dix + dx + d3x dax = -20 km cos 90° day = -20 km sin 90° d2 dax = -30 km cos 0° day = -30 km sin 90° EVy = dty+ dzy + day d3 | Note: Negative signs will be assigned to vectors d2 and da in their x- and y- components because of their direction (South and West) with respect to the origin. STEP 4: Find the resultant vector. A. Magnitude VR = EVx² + EVy² d, = 10 km, 45 NE d, = 20 km, 90S d, = 30 km, O w B. Direction EVx tan e = EVy e = tan-( de de e = da VR = The displacement or the shortest path to get the TREASURE! 7
In this activity, two-dimensional vectors (with x- and y-components) are involved in finding the resultant vector. COMPONENT METHOD will be used to add these vectors. There is a treasure buried in the land of d, = 10 km, 45 NE d, = 20 km, 90S d,= 30 km, O w Physica! And everyone can use the map to get that treasure! Jack wanted to find it first by applying his knowledge in Vector starting pont addition. Can vou help. Jack? de X+ STEP 1: Write all the given information. TREASURE! di = 10 km, 45° NE d2 = 20 km, 90° S d3 = 30 km, 0° W Figure 3. Treasure Map STEP 2: Solve for the x- and y- components. Use your scientific calculator in computation. X-component V = V cos e y-component Vy = V sin 0 Vectors STEP 3: Compute for the summation of Vx and V, dix = 10 km cos 45° dıy = 10 km sin 45° d1 EV = dix + dx + d3x dax = -20 km cos 90° day = -20 km sin 90° d2 dax = -30 km cos 0° day = -30 km sin 90° EVy = dty+ dzy + day d3 | Note: Negative signs will be assigned to vectors d2 and da in their x- and y- components because of their direction (South and West) with respect to the origin. STEP 4: Find the resultant vector. A. Magnitude VR = EVx² + EVy² d, = 10 km, 45 NE d, = 20 km, 90S d, = 30 km, O w B. Direction EVx tan e = EVy e = tan-( de de e = da VR = The displacement or the shortest path to get the TREASURE! 7
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
Problem 2.3CYU: Check Your understanding Using the three displacement vectors A , B , and F in Figure 2.13, choose a...
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Transcribed Image Text:In this activity, two-dimensional vectors (with x- and y-components) are involved in
finding the resultant vector. COMPONENT METHOD will be used to add these vectors.
There is a treasure buried in the land of
d, = 10 km, 45 NE
d, = 20 km, 90 s
d, = 30 km, O w
Physica! And everyone can use the map
to get that treasure! Jack wanted to find it
first by applying his knowledge in Vector
starting point
addition. Can vou help. Jack?
de
STEP 1: Write all the given information.
TREASURE!
di = 10 km, 45° NE
d2 = 20 km, 90° S
d3 = 30 km, 0° W
Figure 3. Treasure Map
STEP 2: Solve for the x- and y-components. Use your scientific calculator in computation.
X-component
Vx = V cos 0
y-component
Vy = V sin e
Vectors
STEP 3: Compute for the
summation of Vx and Vy
dix = 10 km cos 45°
dıy = 10 km sin 45°
di
%3D
%3D
EVx = dix + d2x + d3x
dzx = -20 km cos 90° dzy = -20 km sin 90°
d2
%3D
%3D
dax = -30 km cos 0°
day = -30 km sin 90°
EVy = diy + dzy + day
d3
%3D
| Note: Negative signs will be assigned to vectors dz and
d3 in their x- and y- components because of their
direction (South and West) with respect to the origin.
STEP 4: Find the resultant vector.
A. Magnitude
VR = EVx2 + £Vy2
d, = 10 km, 45' NE
d, = 20 km, 90S
d, = 30 km, O w
B. Direction
EVx
tan 9 =
EVy
e = tan-
EVy
de
de
e =
VR =
The displacement or the shortest
path to get the TREASURE!
7
Figure 4. Map of Jack with Resultant Vector
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