Open Question
(II) At t = 0, a particle starts from rest at 𝓍 = 0 , y = 0 and moves in the xy plane with an acceleration a (→ above a) = (4.0 î + 3.0 ĵ ) m/s². Determine
(a) the 𝓍 and y components of velocity,
3. Vectors
Vector Composition & Decomposition
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A toy gun shoots a plastic ball at an angle of 25° above the horizontal. What is the vertical component of the ball's velocity when it left the gun?
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Verified step by step guidance1
Identify the given values: the initial velocity of the ball \( v = 10 \, \text{m/s} \) and the angle \( \theta = 25^\circ \) above the horizontal.
Understand that the velocity of the ball can be split into two components: horizontal and vertical. We are interested in finding the vertical component of the velocity.
Recall the formula for the vertical component of velocity: \( v_y = v \cdot \sin(\theta) \). This formula uses the sine function because it relates to the opposite side of the angle in a right triangle.
Substitute the given values into the formula: \( v_y = 10 \, \text{m/s} \cdot \sin(25^\circ) \).
Calculate \( \sin(25^\circ) \) using a calculator or trigonometric table, then multiply by 10 m/s to find the vertical component of the velocity.
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