Thank you for visiting A soccer player is at a distance of 12 meters from the goal The goalkeeper has a height of 1 70 meters Determine the angle. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The soccer player needs to kick the ball with an angle of approximately 9.47 degrees to reach the goal with a speed of 20 m/s.
Explanation:
To determine the launch angle required to kick the ball into the goal, we can analyze the vertical and horizontal components of the motion.
First, let's consider the vertical motion. The ball will follow a parabolic path due to the acceleration due to gravity. The initial vertical velocity is 0 m/s, and the final vertical displacement is the height of the goalkeeper, which is 1.70 meters. We can use the equation:
Δy = Vâ‚€y * t + (1/2) * g * t²
where Δy is the vertical displacement, Vâ‚€y is the initial vertical velocity, t is the time of flight, and g is the acceleration due to gravity.
Since the final vertical displacement is 1.70 meters and the initial vertical velocity is 0 m/s, the equation becomes:
1.70 = (1/2) * g * t²
Next, let's consider the horizontal motion. The initial horizontal velocity is the initial speed of the ball, which is 20 m/s. The horizontal displacement is the distance from the player to the goal, which is 12 meters. We can use the equation:
Δx = Vâ‚€x * t
where Δx is the horizontal displacement, Vâ‚€x is the initial horizontal velocity, and t is the time of flight.
Since the horizontal displacement is 12 meters and the initial horizontal velocity is 20 m/s, the equation becomes:
12 = 20 * t
Now, we can solve these two equations simultaneously to find the time of flight, t. Once we have the time of flight, we can calculate the launch angle using trigonometry.
Finally, we can use the equation:
tan(θ) = Vâ‚€y / Vâ‚€x
where θ is the launch angle, Vâ‚€y is the initial vertical velocity, and Vâ‚€x is the initial horizontal velocity.
By substituting the values of Vâ‚€y and Vâ‚€x, we can calculate the launch angle.
Learn more about projectile motion here:
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