Question

A soccer ball was kicked into the air at a speed of 27 miles per hour at an angle of 25° from the horizontal. express this velocity in vector form.

Answer 1

To express the velocity of the soccer ball in vector form, we need to break it down into its horizontal and vertical components. Given the speed is 27 miles per hour and the angle is 25°, the horizontal and vertical components can be calculated using trigonometric functions.

Step-by-step explanation:

To express the velocity of the soccer ball in vector form, we need to break it down into its horizontal and vertical components. The horizontal component can be found using the initial speed and the cosine of the angle, and the vertical component can be found using the initial speed and the sine of the angle.

Given that the speed is 27 miles per hour (which can be converted to 12.08 meters per second) and the angle is 25° from the horizontal, we can calculate the horizontal and vertical components as follows:

1. Horizontal component: 27 mph × cos(25°) = 12.08 m/s × cos(25°) ≈ 10.97 m/s
2. Vertical component: 27 mph × sin(25°) = 12.08 m/s × sin(25°) ≈ 5.26 m/s

Therefore, the velocity of the soccer ball can be expressed in vector form as (10.97 m/s)î + (5.26 m/s)ĵ, where î represents the unit vector in the horizontal direction and ĵ represents the unit vector in the vertical direction.