Final answer:
Using the equations of projectile motion, the horizontal distance traveled by the ball when kicked at a speed of 3 m/s at a 30-degree angle is approximately 1.47 meters.
Step-by-step explanation:
The question asks about the horizontal distance a football travels when kicked at a speed of 3 m/s at an angle of 30 degrees. To solve this, we can use the projectile motion equations. The horizontal distance, also known as the range, of a projectile is given by the formula:
- Range (R) = (v2 × sin(2θ)) / g
where:
- v is the initial velocity,
- θ is the launch angle,
- g is the acceleration due to gravity (9.81 m/s2 on Earth).
Plugging in the values given in the question:
- Initial velocity (v) = 3 m/s,
- Launch angle (θ) = 30 degrees,
- Acceleration due to gravity (g) = 9.81 m/s2.
To find the range, we first need to convert the launch angle to radians as follows: 30 degrees = π/6 radians. We can then calculate the range as follows:
- R = (3 m/s)2 × sin(2 × π/6) / 9.81 m/s2,
- R = 9 × sin(π/3) / 9.81,
- R = 9 × √3/2 / 9.81,
- R ≈ 1.47 meters.
Thus, the ball travels approximately 1.47 meters horizontally from where the placekicker kicks it to where it lands on the ground.