ronaldinho kicks a soccer ball with an initial velocity of 22.0 m/s at an angle of 13.0°. How far away does the ball land?
use the range equation
where Θ is the launch angle ... range = (v^2 / g) * sin(2 Θ)
To find how far away the ball lands, we can use the range formula for projectile motion. The range (horizontal distance) can be calculated using the following equation:
Range = (initial velocity^2 * sin(2*theta)) / g
where:
- initial velocity is the initial velocity of the ball (22.0 m/s)
- theta is the launch angle (13.0°)
- g is the acceleration due to gravity (9.8 m/s^2)
Let's substitute the values into the formula and solve for the range:
Range = (22.0^2 * sin(2*13.0°)) / 9.8
First, let's calculate the value of sin(2*13.0°):
sin(2*13.0°) = sin(26.0°) ≈ 0.438
Now, substitute the values:
Range = (22.0^2 * 0.438) / 9.8
Simplifying further:
Range = (484 * 0.438) / 9.8
Range ≈ 21.66 meters
Therefore, the ball lands approximately 21.66 meters away from the starting point.