To find how far a water balloon fired at 30 m/s at an angle of 50° above the horizontal will travel before it falls to the ground, you can use the following equations of motion.
1. Break the initial velocity into horizontal (Vx) and vertical (Vy) components:
Vx = 30 m/s * cos(50°)
Vy = 30 m/s * sin(50°)
2. Calculate the time it takes for the water balloon to hit the ground. Use the vertical motion equation:
d = (1/2) * g * t^2
Where:
d is the vertical distance (which is what we're trying to find).
g is the acceleration due to gravity (approximately 9.81 m/s²).
t is the time of flight.
Rearrange the equation to solve for t:
t = sqrt((2 * d) / g)
3. Now, we can find d (the vertical distance) using the time calculated above and the horizontal motion equation:
d = Vx * t
Substituting the values we found earlier:
d = (30 m/s * cos(50°)) * sqrt((2 * d) / 9.81 m/s²)
This equation can't be solved directly, but you can use numerical methods or a calculator to find the value of d. The result will be the horizontal distance the water balloon travels before falling to the ground.