Question

I shoot a bullet at a falling cannonball (an indentation that matches the exact shape of the bullet which prevents deformation) how would I graph the trajectory showing it stops before it reverses since the cannonball never stops?

Answer 1

Graphing the trajectory of a bullet shot at a falling cannonball can be done by plotting the position of the bullet over time. However, it's important to note that in this scenario, the bullet will not stop and reverse its motion due to the absence of external forces. Let's assume a simplified scenario for clarity:

1. Choose a coordinate system: Set up a Cartesian coordinate system with the x-axis representing the horizontal direction and the y-axis representing the vertical direction.

2. Determine the initial conditions: Note the initial position (x0, y0) and the initial velocity (vx0, vy0) of the bullet. Let's assume the bullet is initially at rest, so vx0 = 0, and vy0 is the initial upward velocity imparted to counteract the effect of gravity.

3. Determine the acceleration: The bullet experiences two primary forces: gravity acting downwards and the force imparted by the cannonball acting upwards. The net force on the bullet determines its acceleration. Let's assume no other forces (e.g., air resistance) are significant. The acceleration in the x-direction is zero since there are no forces acting horizontally. The acceleration in the y-direction is the acceleration due to gravity, typically represented as -9.8 m/s^2.

4. Solve the equations of motion: Using the initial conditions and the equations of motion, you can determine the position of the bullet (x, y) as functions of time (t). The equations of motion can be solved separately for the x and y directions. Assuming the absence of air resistance, the motion in the x-direction is uniform, and the motion in the y-direction is subject to acceleration due to gravity.

   x(t) = x0 + vx0 * t

   y(t) = y0 + vy0 * t + (1/2) * (-9.8) * t^2

5. Plotting the trajectory: Using the equations above, you can generate a graph that shows the trajectory of the bullet. The x-axis represents time (t), and the y-axis represents the height (y) of the bullet above the ground.

   The graph will show the bullet initially at rest, then it will start to fall due to gravity, and its height will decrease over time until it reaches the ground. The horizontal position (x-coordinate) will continue to increase uniformly since there are no forces acting in that direction.

Note that in this simplified scenario, we are assuming that the bullet's trajectory is not significantly affected by air resistance or other external factors. In reality, these factors can influence the motion of the bullet and the cannonball.