A cannonball is launched at a speed of 30 m/s and at an angle of 60° above the horizontal. What are the magnitudes of the horizontal and vertical components of the cannonball's initial velocity, respectively?

Question

A cannonball is launched at a speed of 30 m/s and at an angle of 60° above the horizontal.  What are the magnitudes of the horizontal and vertical components of the cannonball's initial velocity, respectively?

Quizplus · Accepted Answer

11ecba2d_1323_2e9a_a3bf_8158e98cfcde_MD0008_00 Unlike scalar quantities, vectors contain both a magnitude and a direction. Vectors may be added to or subtracted from other vectors. Consequently, a vector located within a two-dimensional coordinate system can be represented as two vector components in which one vector component is oriented along the x-axis and the other is oriented along the y-axis. Mathematically, the overall (resultant) vector is the hypotenuse (longest side) of a right triangle in which the x- and y-components of the vector form the adjacent and opposite sides. Furthermore, the angle (θ) between the overall vector and its adjacent, horizontal (x-axis) component can be used with trigonometric ratios to calculate the magnitude of the horizontal component (V_x) and vertical component (V_y) of the initial vector (V): 11ecba2d_1323_2e9b_a3bf_5700359cce4a_MD0008_00 11ecba2d_1323_2e9c_a3bf_930696815fce_MD0008_00 In this question, the cannonball is launched with an initial speed of 30 m/s from a cannon angled 60° above the horizontal (ie, the ground). When a convenient orientation is selected for an xy-coordinate system in which the ground is parallel to the x-axis, the cannonball's velocity vector (V) vector is oriented 60° above the x-axis with a magnitude (length) of 30 m/s. Accordingly, the magnitudes of the horizontal (V_x) and vertical components (V_y) of velocity can be calculated as: 11ecba2d_1323_55ad_a3bf_934fb9d8d2f2_MD0008_00 Therefore, the horizontal component of the cannonball's initial velocity has a magnitude of 15 m/s, and the vertical component of the cannonball's initial velocity has a magnitude of 25 m/s (Choice C). Educational objective: Vector quantities can be separated into fundamental component vectors using trigonometric ratios. The horizontal and vertical components of an object's velocity can be calculated using the magnitude of the velocity and its angle above the horizontal.

A Cannonball Is Launched at a Speed of 30 M/s