Projectile Motion - Trajectory

[melle_87@hotmai]

Homework Statement

There is a point A and point B, with 200 m distance between the two. In the center, there is a 100 m wall. What is the minimum velocity (and angle) a ball must be thrown to get over the wall?


Basically I'm clueless. I need step by step instructions.


THANKS!

 

[learningphysics]

What is the vertical velocity required to cross that wall?

 

[m2003]

I would approach this problem by first understanding the concept of projectile motion and trajectory. Projectile motion is the motion of an object through the air under the influence of gravity, and trajectory is the path that the object takes during its motion. In this case, the object is a ball being thrown from point A to point B.

To determine the minimum velocity and angle required for the ball to clear the 100 m wall, we can use the equations of projectile motion. These equations take into account the initial velocity, angle of projection, and the effects of gravity on the object's motion.

Step 1: Draw a diagram of the scenario, labeling the points A and B, as well as the distance between them (200 m) and the height of the wall (100 m).

Step 2: Identify the known values in the problem. In this case, we know the distance between the points, the height of the wall, and the acceleration due to gravity (9.8 m/s^2).

Step 3: Use the following equations to solve for the minimum velocity and angle:
- Horizontal distance (x) = initial velocity (V0) * time (t) * cosine(angle)
- Vertical distance (y) = initial velocity (V0) * time (t) * sine(angle) - (1/2) * acceleration due to gravity * time^2
- Total time of flight = 2 * V0 * sine(angle) / acceleration due to gravity

Step 4: Substitute the known values into the equations and solve for the minimum velocity and angle. For example, if we assume an angle of 45 degrees, we can solve for the minimum initial velocity required to clear the wall.

Step 5: Use a trial and error method to adjust the angle until the calculated initial velocity is the minimum required to clear the wall.

Step 6: Once the minimum velocity and angle have been determined, double check your calculations and make sure they are consistent with the known values and the laws of physics.

In conclusion, to determine the minimum velocity and angle required for a ball to clear a 100 m wall at a distance of 200 m, we would use the equations of projectile motion and a trial and error method to solve for the desired values. It is important to understand the concepts of projectile motion and trajectory in order to approach and solve this problem accurately.