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In the following answer to the below question how did U → = (5 cos(20°) , 5 sin(20°)) come..what is the formula used?? QUES- The magnitudes of two vectors U and V are equal to 5 and 8 respectively. Vector U makes an angle of 20° with the positive direction of the x-axis and vector V makes an angle of 80° with the positive direction of the x-axis. Both angles are measured counterclockwise. Find the magnitudes and directions of vectors U + V and U - V. SOLUTION - Let us first use the magnitudes and directions to find the components of vectors U and V. U → = (5 cos(20°) , 5 sin(20°)

In the following answer to the below question how did U → = (5 cos(20°) , 5 sin(20°))  come..what is the formula used??
QUES-The magnitudes of two vectors U and V are equal to 5 and 8 respectively. Vector U makes an angle of 20° with the positive direction of the x-axis and vector V makes an angle of 80° with the positive direction of the x-axis. Both angles are measured counterclockwise. Find the magnitudes and directions of vectors U + V and U - V. 
SOLUTION -Let us first use the magnitudes and directions to find the components of vectors U and V. 
U → = (5 cos(20°) , 5 sin(20°)

Grade:11

2 Answers

Arun
25750 Points
5 years ago
Dear student
 
here velocity is divided in two components named horizontal component (5 cos 20) and vertical component (5 sin20)
Piyush Kumar Behera
417 Points
5 years ago
In the above solution posted for the question actually resolves the vector U into horizontal and vertical componesnt.
To make it more clear,
The horizontal component of any vector can be found out by multiplying the magnitude of the vector multiplied the cos of the angle made by the horizontal.
Similarly,The vertical component of any vector can be found out by multiplying the magnitude of the vector multiplied the sine of the angle made by the horizontal.
Here the values given in the brackets are horizontal and vertical components of the vector.
To solve the question ,
resolve U and V into horizontal and vertical components and add it as rectangular componests(i.e in terms of i and j)
Then add and subtract accordingly and find resaultant to get the answer of the question.
Hope it helps!!
 
Piyush Kumar Behera
IIT  (ISM) Dhanbad

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