Throwing a ball in a 2D projectile motion and lands on an inclined plane

Thread starter dhagstk
Start date Jan 18, 2012
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2d Ball Inclined Inclined plane Motion Plane Projectile Projectile motion

In summary, the initial velocity of a ball in 2D projectile motion can be calculated using the formula v = √(gx^2 + 2gh). The trajectory of the ball can be described by the equation y = xtanθ - (gx^2 / 2v^2cos^2θ), and the angle of the inclined plane affects the motion by changing the acceleration due to gravity. The time of flight can be calculated using t = (2v sinθ)/g, and the initial velocity can be adjusted to reach a specific point on the inclined plane by changing the launch angle and initial speed of the ball.

Jan 18, 2012

dhagstk

Attached is an image showing the problem. Supposed the β, θ, and √o are given. How do we get the distance from the initial position of the ball to the final position on the inclined plane?

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Jan 18, 2012

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1. How do you calculate the initial velocity of a ball in 2D projectile motion?

The initial velocity of a ball in 2D projectile motion can be calculated using the formula v = √(gx^2 + 2gh), where g is the acceleration due to gravity, x is the horizontal distance, and h is the vertical distance.

2. What is the equation for the trajectory of a ball in 2D projectile motion?

The trajectory of a ball in 2D projectile motion can be described by the equation y = xtanθ - (gx^2 / 2v^2cos^2θ), where y is the vertical displacement, x is the horizontal displacement, θ is the launch angle, and v is the initial velocity.

3. How does the angle of the inclined plane affect the motion of the ball?

The angle of the inclined plane affects the motion of the ball by changing the acceleration due to gravity. As the angle increases, the vertical component of gravity decreases, causing the ball to accelerate less and travel a shorter distance on the inclined plane.

4. How do you calculate the time of flight for a ball in 2D projectile motion?

The time of flight for a ball in 2D projectile motion can be calculated using the formula t = (2v sinθ)/g, where v is the initial velocity and θ is the launch angle.

5. Can the initial velocity of the ball be changed to make it reach a specific point on the inclined plane?

Yes, the initial velocity of the ball can be changed to make it reach a specific point on the inclined plane. This can be done by adjusting the launch angle and initial speed of the ball, using the equations mentioned above, to achieve the desired trajectory and landing point on the inclined plane.