Christiano Ronaldo kicks a soccer ball with an initial velocity of 24.0 m/s at an angle of 25.0°. How far away does the ball land?
To find the distance at which the ball lands, we can use the equations of projectile motion. Here's how you can solve it:
Step 1: Resolve the initial velocity into its horizontal and vertical components. The horizontal component (Vx) can be found using the equation Vx = V * cos(θ), where V is the initial velocity (24.0 m/s in this case) and θ is the angle of the kick (25.0°). The vertical component (Vy) can be found using the equation Vy = V * sin(θ).
Vx = 24.0 m/s * cos(25.0°) = 21.69 m/s
Vy = 24.0 m/s * sin(25.0°) = 10.20 m/s
Step 2: Find the time of flight (t). The time of flight is the time it takes for the ball to reach its highest point and then return back to the ground, assuming no air resistance. The time of flight can be found using the equation t = 2 * (Vy / g), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
t = 2 * (10.20 m/s / 9.8 m/s^2) = 2.08 s
Step 3: Determine the horizontal distance traveled (d). The horizontal distance is given by the equation d = Vx * t.
d = 21.69 m/s * 2.08 s = 45.10 m
Therefore, the ball lands approximately 45.10 meters away from the point of kick.
the range
R = v^2/g sin2θ
Now just plug in your values