"How far would a tennis ball (100g) go if thrown from your catapult at a height of 1m with a force of 50 N and at an angle of 50 degrees from the horizontal?"

I do not know. It depends how long you sustained the 50 N force.

the potential elastic energy can not be found so it is impossible to calc. The kinetic energy of the body

To determine how far a tennis ball would go when thrown from a catapult with the given specifications, we can use the principles of projectile motion. Here's how you can calculate it:

Step 1: Resolve the force into its horizontal and vertical components:
The horizontal component of the force can be calculated using the formula: F_horizontal = F × cos(θ), where F is the force (50 N) and θ is the angle (50 degrees).
F_horizontal = 50 N × cos(50°)

Step 2: Calculate the initial velocity in the horizontal direction:
The initial velocity in the horizontal direction (Vx) is the horizontal component of the force.
Vx = F_horizontal

Step 3: Calculate the initial velocity in the vertical direction:
The vertical component of the force can be calculated using the formula: F_vertical = F × sin(θ), where F is the force (50 N) and θ is the angle (50 degrees).
F_vertical = 50 N × sin(50°)

Step 4: Calculate the initial velocity in the vertical direction:
The initial velocity in the vertical direction (Vy) can be calculated using the formula: Vy = F_vertical / mass, where mass is the mass of the tennis ball (100g) converted to kg.
Vy = (50 N × sin(50°)) / 0.1 kg

Step 5: Calculate the total initial velocity:
The total initial velocity (V) can be calculated using the Pythagorean theorem: V = √(Vx^2 + Vy^2).
V = √(Vx^2 + Vy^2)

Step 6: Calculate the time of flight:
The time of flight (t) can be calculated using the vertical component of the initial velocity: t = 2 × Vy / g, where g is the acceleration due to gravity (9.8 m/s^2).
t = 2 × Vy / 9.8 m/s^2

Step 7: Calculate the horizontal distance:
The horizontal distance (d) can be calculated using the formula: d = Vx × t.
d = Vx × t

Now, let's plug in the values and calculate the answer:

First, let's calculate F_horizontal:
F_horizontal = 50 N × cos(50°)

Next, let's calculate Vx:
Vx = F_horizontal

Now, let's calculate F_vertical:
F_vertical = 50 N × sin(50°)

Next, let's calculate Vy:
Vy = (F_vertical) / 0.1 kg

Now, let's calculate V:
V = √(Vx^2 + Vy^2)

Next, let's calculate t:
t = 2 × Vy / 9.8 m/s^2

Finally, let's calculate d:
d = Vx × t

By following these steps and plugging in the values, you will get the answer for how far the tennis ball would go.