two stones with initial speeds of 13 m/s and are thrown at an angle 30 degrees, one below the horizontal and one above the horizontal. What is the distance between the points where the stones strike the ground?

To find the distance between the points where the stones strike the ground, we can use the equations of motion and the given information about the stones' initial velocities and angles.

Let's consider each stone separately:

1. Stone below the horizontal:
The initial velocity of this stone is 13 m/s at an angle of 30 degrees below the horizontal. Since the angle is below the horizontal, we can decompose the velocity into horizontal and vertical components.

The horizontal component (Vx) can be found using the equation:
Vx = V * cos(angle)
Vx = 13 m/s * cos(30 degrees)
Vx = 13 m/s * sqrt(3)/2
Vx ≈ 11.26 m/s

The vertical component (Vy) can be found using the equation:
Vy = V * sin(angle)
Vy = 13 m/s * sin(30 degrees)
Vy = 13 m/s * 1/2
Vy = 6.5 m/s

Now, let's find the time taken by the stone to reach the ground. We can use the vertical component of the velocity.

The equation used to find the time (t) is:
y = Vy * t + (1/2) * g * t^2
0 = 6.5 m/s * t + (1/2) * 9.8 m/s^2 * t^2
0 = 9.8 m/s^2 * t^2 + 6.5 m/s * t

Solving this quadratic equation will give us the time taken by the stone to reach the ground.

Once we have the time, we can find the horizontal distance traveled by the stone using the equation:
x = Vx * t

2. Stone above the horizontal:
For the stone thrown above the horizontal, the vertical component of the velocity will be negative, since it is thrown upwards. The horizontal component remains the same.

Repeat the above steps with the negative value of the vertical component (Vy = -6.5 m/s) to find the time taken and the horizontal distance traveled by this stone.

Finally, to find the distance between the points where the stones strike the ground, subtract the horizontal distance of the stone thrown above the horizontal from the horizontal distance of the stone thrown below the horizontal.

Distance between the points = Horizontal distance (stone below horizontal) - Horizontal distance (stone above horizontal)