Accepted Answer
First draw a picture to help make the problem easier. (see attached)Next you can use sin and cos to find the x and y components of the velocity.First lets find the vertical component:[tex]sin = \frac{opp}{hyp} [/tex][tex]sin(60) = \frac{y}{15m/s} [/tex]Multiply both sides by 15m/s[tex]15m/s * sin(60) = y[/tex]y ≈ 13 m/sNow you can find the horizontal component:[tex]cos = \frac{adj}{hyp} [/tex][tex]cos(60) = \frac{x}{15m/s} [/tex]Multiply both sides by 15m/s[tex]15m/s * cos(60) - x[/tex]x = 7.5Therefore the answer is 2, the vertical (y) component is 13m/s and the horizontal (x) component is 7.5m/s.
Suggested Answer
The components of the velocity are :(2) 13 m/s vertical and 7.5 m/s horizontal[tex]\texttt{ }[/tex]Further explanationVector 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.[tex]\texttt{ }[/tex]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![tex]\texttt{ }[/tex]Given:magnitude of the velocity = v = 15 m/sdirection 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][tex]\texttt{ }[/tex]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][tex]\texttt{ }[/tex]Learn moreVelocity of Runner : https://brainly.com/question/3813437Kinetic Energy : https://brainly.com/question/692781Acceleration : https://brainly.com/question/2283922The Speed of Car : https://brainly.com/question/568302Magnitude of A Vector : https://brainly.com/question/2678571[tex]\texttt{ }[/tex]Answer detailsGrade: High SchoolSubject: PhysicsChapter: Vectors
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