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The components of the velocity are :
(2) 13 m/s vertical and 7.5 m/s horizontal
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Vector is a quantity that has a magnitude and direction.
A vector in a cartesian coordinate is represented by an arrow in which the slope of the arrow shows the direction of the vector and the length of the arrow shows the magnitude of the vector.
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A position vector of a point is a vector drawn from the base point of the coordinates O (0,0) to that point.
The addition of two vectors can be done in the following ways:
[tex]\overrightarrow {AB} + \overrightarrow {BC} = \overrightarrow {AC}[/tex]
A negative vector is a vector with the same magnitude but in opposite direction.
[tex]\overrightarrow {AB} = -\overrightarrow {BA}[/tex]
Let's tackle the problem!
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Given:
magnitude of the velocity = v = 15 m/s
direction of the velocity = θ = 60°
Asked:
horizontal component of the velocity = v_x = ?
vertical component of the velocity = v_y = ?
Solution:
Firstly , we will calculate the horizontal component of the velocity as follows:
[tex]v_x = v \cos \theta[/tex]
[tex]v_x = 15 \times \cos 60^o[/tex]
[tex]v_x = 15 \times \frac{1}{2}[/tex]
[tex]\boxed {v_x = 7.5 \texttt{ m/s}}[/tex]
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Next , we will calculate the vertical component of the velocity as follows:
[tex]v_y = v \sin \theta[/tex]
[tex]v_y = 15 \times \sin 60^o[/tex]
[tex]v_y = 15 \times \frac{1}{2} \sqrt{3}[/tex]
[tex]v_y = 7.5 \sqrt{3} \texttt{ m/s}[/tex]
[tex]\boxed {v_y \approx 13 \texttt{ m/s}}[/tex]
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Grade: High School
Subject: Physics
Chapter: Vectors
