Final answer:
To find the height at which the water strikes the building, we can use the equations of motion for the vertical direction. By calculating the vertical component of the initial velocity and using the formula for height, we can determine that the water strikes the building at a height of approximately 28.5 meters.
Step-by-step explanation:
To find the height at which the water strikes the building, we need to determine the vertical component of the water's initial velocity. We can start by finding the horizontal and vertical components of the initial velocity using the given angle. We know that the initial speed is 34.0 m/s and the angle is 19.0°.
The vertical component of the initial velocity can be found using the formula: vertical component = initial speed * sin(angle). Plugging in the values, we get vertical component = 34.0 m/s * sin(19.0°). Calculating this gives us a value of 11.3 m/s.
Now, we can use the equation of motion for the vertical direction to find the height at which the water strikes the building. The equation is: final height = initial height + (vertical component * time) - (0.5 * acceleration * time^2). Since the water starts from the ground, the initial height is 0. The acceleration due to gravity is -9.8 m/s^2 (negative because it acts downwards). We can assume the time it takes for the water to reach the building is the same as the time it takes for the water to hit the ground when launched vertically. Using the equation, we have: final height = 0 + (11.3 m/s * time) - (0.5 * -9.8 m/s^2 * time^2). Solving for the time, we find that it takes approximately 2.3 seconds for the water to reach the building. Plugging this value back into the equation, we can find the final height: final height = 0 + (11.3 m/s * 2.3 s) - (0.5 * -9.8 m/s^2 * (2.3 s)^2). After calculating, we get a final height of approximately 28.5 meters.