A person who is 1.4 m tall throws a ball with a speed of 4.2 m/s at an angle of 25 degrees above the horizontal. What are the x and y components of the velocity (in m/s) of the ball the instant before it strikes the ground? The acceleration due to gravity is 10 m/s2
To find the x and y components of the velocity of the ball, we can break down the initial velocity into horizontal and vertical components.
The horizontal component (Vx) represents the velocity in the x-axis direction (parallel to the ground), and the vertical component (Vy) represents the velocity in the y-axis direction (perpendicular to the ground).
Given:
Initial speed of the ball (V) = 4.2 m/s
Angle above the horizontal (θ) = 25 degrees
Acceleration due to gravity (g) = 10 m/s^2
To find Vx:
Vx = V * cos(θ)
To find Vy:
Vy = V * sin(θ)
Let's calculate Vx and Vy:
Vx = 4.2 m/s * cos(25 degrees) = 4.2 m/s * 0.90631 ≈ 3.80 m/s
Vy = 4.2 m/s * sin(25 degrees) = 4.2 m/s * 0.42336 ≈ 1.78 m/s
Therefore, the x-component of the velocity (Vx) of the ball is approximately 3.80 m/s, and the y-component of the velocity (Vy) is approximately 1.78 m/s.
To determine the x and y components of the velocity of the ball before it strikes the ground, we can use the following equations:
Initial velocity in the x direction (Vx) = V * cos(θ)
Initial velocity in the y direction (Vy) = V * sin(θ)
where V is the speed of the ball and θ is the angle above the horizontal.
Given:
Speed of the ball (V) = 4.2 m/s
Angle (θ) = 25 degrees
Using the equations above, we can calculate the x and y components of the velocity:
Vx = 4.2 m/s * cos(25°)
Vy = 4.2 m/s * sin(25°)
Now let's calculate each component:
Vx = 4.2 m/s * cos(25°) ≈ 3.771 m/s
Vy = 4.2 m/s * sin(25°) ≈ 1.796 m/s
Therefore, the x component of the velocity (Vx) is approximately 3.771 m/s, and the y component of the velocity (Vy) is approximately 1.796 m/s.