The Horizontal Component of Initial Velocity in Projectile Motion
A soccer player kicks a ball with an initial velocity of 10 meters per second at an angle of 30 ° above the horizontal.
The magnitude of the horizontal component of the ball’s initial velocity is,
Final answer: The magnitude of the horizontal component of the ball's initial velocity is 8.66 m/s.
Explanation: In projectile motion, an object is launched into the air with an initial velocity and follows a curved path under the influence of gravity. The motion can be divided into horizontal and vertical components. The horizontal component of the initial velocity determines the object's motion along the x-axis, while the vertical component determines its motion along the y-axis.
To find the magnitude of the horizontal component of the ball's initial velocity, we can use the equation:
horizontal component = initial velocity * cos(angle)
Given that the initial velocity is 10 meters per second and the launch angle is 30° above the horizontal, we can substitute these values into the equation:
horizontal component = 10 m/s * cos(30°)
Using a calculator, we can find the cosine of 30° to be approximately 0.866. Therefore, the magnitude of the horizontal component of the ball's initial velocity is:
horizontal component = 10 m/s * 0.866 = 8.66 m/s
Question:
What is the magnitude of the horizontal component of the ball’s initial velocity when a soccer player kicks a ball with an initial velocity of 10 meters per second at an angle of 30 ° above the horizontal?
Answer:
The magnitude of the horizontal component of the ball’s initial velocity will be approximately 8.66 meters per second when a soccer player kicks a ball with an initial velocity of 10 meters per second at an angle of 30 ° above the horizontal.
To find the horizontal component of the ball's initial velocity, we can use trigonometric functions since the angle is given. The horizontal and vertical components of the initial velocity can be calculated as follows:
Horizontal component (Vx) = Initial velocity * cos(angle)
Vertical component (Vy) = Initial velocity * sin(angle)
Given:
Initial velocity = 10 meters per second
Angle = 30 degrees
Horizontal component (Vx) = 10 m/s * cos(30°)
Horizontal component (Vx) = 10 m/s * (√3/2)
Horizontal component (Vx) = 5√3 m/s
So, the magnitude of the horizontal component of the ball's initial velocity is approximately 8.66 meters per second.