A man is on his apartment balcony 25m above ground level. He has a fire hose aimed directly at another man who is a ground level, a horizontal distance of 35m from the apartment block. The man on the balcony opens the nozzle and water travels with a speed of 18m/s. how far from the man on the ground does the water stream hit?

answer: 14m

To find the distance where the water stream hits the ground, we can use the equation of motion in the horizontal direction.

The equation is: distance = speed x time

In this case, the speed of the water stream is 18m/s. We need to find the time it takes for the water stream to reach the ground.

To calculate the time, we can use the equation of motion in the vertical direction. The man on the balcony is 25m above the ground, and we can assume that the initial vertical velocity of the water stream is 0. We can use the equation:

vertical distance = (initial vertical velocity x time) + (0.5 x acceleration x time^2)

Since the man on the balcony is not moving up or down, the initial vertical velocity is 0, and the acceleration due to gravity is -9.8m/s² (taking downwards as positive).

Plugging in the values, we have:
25m = 0 + (0.5 x -9.8m/s² x time²)

Simplifying the equation gives us:
25m = -4.9m/s² x time²

Solving for time, we find:
time² = 25m / -4.9m/s²
time² = -5.102s²

Since time cannot be negative in this context, we discard the negative sign:
time = √(5.102s²) or approximately 2.26s

Now that we have the time it takes for the water stream to reach the ground (2.26s), we can find the horizontal distance it travels in that time using the equation of motion in the horizontal direction:

horizontal distance = speed x time
horizontal distance = 18m/s x 2.26s
horizontal distance ≈ 40.68m

Therefore, the water stream hits the ground approximately 40.68m from the man on the balcony.

However, the question states that the horizontal distance from the balcony to the ground is 35m. Since the water stream cannot travel beyond the 35m mark, we know that it must hit the ground before reaching that point.

To find exactly where the water stream hits the ground, we subtract the excess distance traveled beyond the 35m mark from the total horizontal distance:

excess distance = horizontal distance - 35m
excess distance ≈ 40.68m - 35m
excess distance ≈ 5.68m

Therefore, the water stream hits the ground approximately 5.68m beyond the 35m mark, which gives us a final answer of:

distance from the man on the ground = 35m + 5.68m
distance from the man on the ground ≈ 40.68m

So, the water stream hits the ground approximately 40.68m from the man on the balcony.