a ball is kicked at an inertial the velocity to 15m/s at an angle of 53 degree to the horizontal calculate the inertia horizontal and vertical velocity.
To calculate the horizontal and vertical velocities of the ball after it is kicked, we can use trigonometry.
Given:
Initial velocity (v₀) = 15 m/s
Angle (θ) = 53 degrees
Horizontal Velocity (vₓ):
The horizontal velocity remains constant throughout the motion because there is no acceleration in the horizontal direction. So, the horizontal velocity (vₓ) remains the same as the initial velocity (v₀).
vₓ = v₀ = 15 m/s (horizontal velocity)
Vertical Velocity (vᵥ):
To find the vertical velocity, we need to determine its component along the vertical axis. Since there is no acceleration in the horizontal direction, the vertical velocity is affected only by gravity. We can use the following formula to find the vertical velocity (vᵥ):
vᵥ = v₀ * sin(θ)
Where:
sin(θ) = the sine of the angle θ (53 degrees)
Substituting the values:
vᵥ = 15 m/s * sin(53°)
Using a scientific calculator or the trigonometric function on your calculator, calculate sin(53°), which is approximately 0.7986.
vᵥ ≈ 15 m/s * 0.7986 ≈ 11.979 m/s (vertical velocity)
Therefore, the horizontal velocity is 15 m/s, and the vertical velocity is approximately 11.979 m/s.