Final answer:
To hit a plant 7.15 meters away, we need to apply projectile motion principles, assuming a 45-degree angle for maximum range and solving for the initial speed needed to overcome gravity's pull. The formula used is R = (v^2 × sin(2θ)) / g.
Step-by-step explanation:
If the gardener wants a stream of water to hit a plant 7.15 meters away horizontally, we need to employ principles from projectile motion to find the necessary speed of the water at point 1. Using the formula for the range of a projectile (R = (v^2 × sin(2θ)) / g), where g is the acceleration due to gravity and θ is the launch angle. Assuming the water is projected at an angle that maximizes the range, which is 45 degrees, and the only acceleration acting on the water is gravity (9.8 m/s^2), we can rearrange to solve for the speed (v).
At 45 degrees, sin(2θ) equals 1, simplifying the formula to R = v^2 / g. Plugging in 7.15 meters for R and 9.8 m/s^2 for g, we get v^2 = R × g, which leads to v = √(R × g). By solving for v, we can determine the exact speed of the water flow
needed at point 1 to cover the distance. Here, we're ignoring air resistance and assuming a purely parabolic trajectory.
The exact numerical answer would require calculation, but the process described would help the student find the solution.