8 Common Questions of Vectors
- Category: High School
- Written by fisikastudycenter
physics.fisikastudycenter.com- 8 common problem of vectors, finding the vectors resultant with some different methods.
Problem 1
Given two vectors with magnitudes both of them are 10 Newton.
Given two vectors with magnitudes both of them are 10 Newton.
The angle between two vectors is 60°, find the resultant!
Solution
Using direct formula for the case two vectors with an angle of θ the vector resultant R is given by
Problem 2
Given two vectors as shown in the figure below!
Given two vectors as shown in the figure below!
Find the vector resultant R, a side of box represents 10 N!
Solution
Project each vector to its components at x and y axis, and sum the vector components both x and y axis then get the resultant:
Problem3
Three vectors that are F1=10 N, F2=25 N dan F3=15 N as our figure below.
Three vectors that are F1=10 N, F2=25 N dan F3=15 N as our figure below.
Find:
a. the vector resultant
a. the vector resultant
b. the direction of vector resultant refering to x axis.
[Sin 37° = (3/5), Sin 53° = (4/5)]
Solution
a. Follow these steps:
1. Project each vector to its components
2. Sum the x components
3. Sum the y components
4. Insert sum of x and y
b. Finding the resultant direction
Problem 4
Two vectors with the same magnitudes of F. The ratio between the addition and difference of both vectors is √3, find the angle that is formed by the two vectors!
Two vectors with the same magnitudes of F. The ratio between the addition and difference of both vectors is √3, find the angle that is formed by the two vectors!
Solution
The sum and difference of borh vectors respectively:
The ratio is √3
and then
we get
Problem 5
Sebuah perahu menyeberangi sungai yang lebarnya 180 m dan kecepatan airnya 4 m/s. Bila perahu diarahkan menyilang tegak lurus dengan kecepatan 3 m/s, tentukan panjang lintasan yang ditempuh perahu hingga sampai ke seberang sungai! (Sumber Soal : UMPTN)
and then
we get
Problem 5
Sebuah perahu menyeberangi sungai yang lebarnya 180 m dan kecepatan airnya 4 m/s. Bila perahu diarahkan menyilang tegak lurus dengan kecepatan 3 m/s, tentukan panjang lintasan yang ditempuh perahu hingga sampai ke seberang sungai! (Sumber Soal : UMPTN)
Pembahasan
Using phytagorean and comparing the sides of triangles ABC and ADE then we get
Problem 6
Given three vectors as shown in figure below
The magnitude of vector resultant is ...
A. 2,0 N
B. 2 √3 N
C. 3,0 N
D. 3 √3 N
E. 4√3 N
Solution
Use your own methode and the answer is 3 N
Problem 7
Given three vectors below :
a = 2i + 3j unit
b = 4i + 5j unit
c = 6i + 7j unit
Find the vector resultant and the direction!
Data:
Problem 8
Given three vectors that are a, b, c .
Using polygon method show :
(i) d = a + b + c
(ii) d = a + b − c
(iii) d = a − b + c
Solution
Polygon method :
(i) d = a + b + c
(ii) d = a + b − c
(iii) d = a − b + c
prepared : fisikastudycenter.com