a football place kicker kicks the ball with a velocity of 18.2 m/s at an angle of 53 degrees. how far from the kicker will the football hit the ground?
To find the horizontal distance the football will travel before hitting the ground, you can use the kinematic equation:
d = (v^2 * sin(2θ)) / g
Where:
- d is the horizontal distance traveled by the football (what we are trying to find)
- v is the initial velocity of the football (18.2 m/s)
- θ is the launch angle of the football (53 degrees)
- g is the acceleration due to gravity (9.8 m/s^2)
Now let's plug in the values and solve for d:
d = (18.2^2 * sin(2 * 53)) / 9.8
First, calculate the value inside the bracket:
sin(2 * 53) = sin(106) ≈ 0.927
Now substitute the values:
d = (18.2^2 * 0.927) / 9.8
Next, calculate the value inside the first bracket:
18.2^2 * 0.927 ≈ 287.017
Now divide by 9.8 to find the distance:
d ≈ 287.017 / 9.8 ≈ 29.285
Therefore, the football will hit the ground approximately 29.3 meters away from the kicker.