Tiffany throws a ball with a velocity of 5 m/s. As soon as it leaves her hand, the ball makes an angle of 30 ° with the ground. What are the x and y components of the velocity of the ball?
To find the x and y components of the velocity, we need to decompose the given velocity vector into its horizontal (x) and vertical (y) components.
The x component of the velocity represents the motion in the horizontal direction, and the y component represents the motion in the vertical direction.
We can use trigonometry to find these components. In this case, we have the magnitude of the velocity (5 m/s) and the angle it makes with the ground (30°).
The x component of the velocity can be found using the formula:
Vx = V * cos(θ), where V is the magnitude of the velocity and θ is the angle it makes with the ground.
Substituting the given values, we get:
Vx = 5 m/s * cos(30°)
Using the trigonometric identity cos(30°) = √3/2, we can calculate the x component:
Vx = 5 m/s * √3/2 = 2.5√3 m/s
Similarly, the y component of the velocity can be found using the formula:
Vy = V * sin(θ), where V is the magnitude of the velocity and θ is the angle it makes with the ground.
Substituting the values:
Vy = 5 m/s * sin(30°)
Using the trigonometric identity sin(30°) = 1/2, we can calculate the y component:
Vy = 5 m/s * 1/2 = 2.5 m/s
Therefore, the x component of the velocity (horizontal component) is 2.5√3 m/s, and the y component of the velocity (vertical component) is 2.5 m/s.