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Determining Longest Distance Traveled by a Player in a Vector Diagram, Assignments of Physics

Physics

A solution to a performance task involving the determination of the longest distance traveled by a player in a vector diagram. The task involves calculating the net displacement of each player by adding the components of their individual vectors and finding the magnitude and direction of the resultant vector. The document also includes the coordinates of each player and the equations used to find the resultant vector.

Typology: Assignments

2020/2021

Uploaded on 12/13/2021

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ALONDATA, NESTOR GABRIEL B. NOVEMBER 11, 2021
12 – QUISUMBING B2
PERFORMANCE TASK 1
Vectors
Who among players A, B, and C has traveled the longest distance? Determine the magnitude and
direction of each player’s net displacement. Draw the vectors using the tail-to-tip method inside
the rectangle. Use approximations if vectors cannot be drawn to scale. Show your complete
solution in the space provided. Use additional sheet if necessary. If final answers are not whole
number, round them off to 2 decimal places.
1. Coordinates of Player A
a. 14 units W
b. 22 units S
c. 12.80624847 units,51.34° S of E
Diagram:
Solution:
Components:
a
󰇍
:(xa,ya)= (−14,0)
b
󰇍
:(xb,yb)= (0, −22)
c :(xc,yc)= (xc,yc)
Equations to be used:
• xr= xa+xb+ xc= xa+ 0 +xc= xa+ xc
• yr= ya+yb+yc= 0 + yb+yc= yb+ yc
• r =√(xr)2+(yr)2
• θ1=tan−1 (xr
yr)
• θ2=90°− θ1
RTF:
Components of c
Components of (r )
Resultant vector (r )
cos51.34° = xc
12.80624847, xc=12.80624847cos 51.34°
sin51.34° = − yC
12.80624847,yc= −12.80624847sin51.34°
𝐜
:(𝐱𝐜,𝐲𝐜)=(𝟖.𝟎𝟎𝟎𝟎𝟑,−𝟗.𝟗𝟗𝟗𝟗𝟕)
xr= xa+xc= −14 +8.00003 = −𝟓. 𝟗𝟗𝟗𝟗𝟕 𝐮𝐧𝐢𝐭𝐬
yr= yb+𝑦𝑐= −22−9.99997 = −𝟑𝟏.𝟗𝟗𝟗𝟗𝟕 𝐮𝐧𝐢𝐭𝐬
r =√(−5.99997 units)2+(−31.99997 units)2≈𝟑𝟐.𝟓𝟔 𝐮𝐧𝐢𝐭𝐬
θ1=tan−1 (xr
yr)≈𝟏𝟎.𝟔𝟐° 𝐖 𝐨𝐟 𝐒
θ2=90°− θ1=𝟕𝟗.𝟑𝟖° 𝐒 𝐨𝐟 𝐖
pf3
pf4

Partial preview of the text

Download Determining Longest Distance Traveled by a Player in a Vector Diagram and more Assignments Physics in PDF only on Docsity!

ALONDATA, NESTOR GABRIEL B. NOVEMBER 11, 2021

12 – QUISUMBING B

PERFORMANCE TASK 1

Vectors

Who among players A, B, and C has traveled the longest distance? Determine the magnitude and

direction of each player’s net displacement. Draw the vectors using the tail-to-tip method inside

the rectangle. Use approximations if vectors cannot be drawn to scale. Show your complete

solution in the space provided. Use additional sheet if necessary. If final answers are not whole

number, round them off to 2 decimal places.

  1. Coordinates of Player A

a. 14 units W

b. 22 units S

c. 12. 80624847 units, 51 .34° S of E

Diagram:

Solution:

Components:

a⃑ : (x

a

, y

a

b

x

b

, y

b

c: (x

c

, y

c

) = (x

c

, y

c

Equations to be used:

  • x

r

= x

a

  • x

b

  • x

c

= x

a

  • 0 + x

c

= x

a

  • x

c

  • y

r

= y

a

  • y

b

  • y

c

= 0 + y

b

  • y

c

= y

b

  • y

c

  • r = √(x

r

2

  • (y

r

2

  • θ

1

= tan

− 1

x

r

y

r

  • θ

2

= 90° − θ

1

RTF:

Components of c

Components of (r)

Resultant vector (r)

cos 51. 34 ° =

x

c

, x

c

= 12. 80624847 cos 51. 34 °

sin 51. 34 ° = −

y

C

, y

c

= − 12. 80624847 sin 51. 34 °

𝐜

𝐜

x

r

= x

a

  • x

c

y

r

= y

b

𝑐

r =

− 5. 99997 units

2

− 31. 99997 units

2

θ

1

= tan

− 1

x

r

y

r

θ

2

= 90° − θ

1

  1. Coordinates of Player B

a. 12. 08304597 units, 65 .56° S of E

b. 8 units E

c. 13 units N

d. 2 units E

Diagram:

Solution:

Components:

a⃑ :

x

a

, y

a

= (x

a

, y

a

b

: (x

b

, y

b

c: (x

c

, y

c

d

: (x

d

, y

d

Equations to be used:

  • x

r

= x

a

  • x

b

  • 0 + x

d

= x

a

  • x

b

  • x

d

  • y

r

= y

a

  • 0 + y

c

  • 0 = y

a

  • y

c

  • r = √(x

r

2

  • (y

r

2

  • θ

1

= tan

− 1

x

r

y

r

  • θ

2

= 90° − θ

1

RTF:

Components of a⃑

Components of (r)

Resultant vector (r)

cos 65. 56 ° =

x

a

, x

a

= 12. 08304597 cos 65. 56 °

sin 65. 56 ° = −

y

a

, y

a

= − 12. 08304597 sin 65. 56 °

𝐚

𝐚

x

r

= x

a

  • x

b

  • x

d

y

r

𝑎

𝑐

r = √( 14. 99924 units)

2

  • ( 2. 00035 units)

2

θ

1

= tan

− 1

x

r

y

r

θ

2

= 90° − θ

1

iii. Total distance travelled by Player C ≈ 𝟒𝟖. 𝟖𝟏 𝐮𝐧𝐢𝐭𝐬

b. Thus, the longest distance is travelled by both players A and C with a

magnitude of 48.81 units.