A stream of water emerges horizontally from firehouse at velocity of 15.0 m/s. If the nozzle is 10.0 m above the ground, find

a. the time required for the water to reach the ground
b. the horizontal distance traveled by the water

A. 1.43

a. h = g*t^2.

10.0 = 9.8t^2, t = ?.

b. Xo = 15 m/s.
d = Xo * t.

a. Well, let's calculate the time it takes for the water to reach the ground. We can use the equation for vertical motion:

d = v_i * t + (1/2) * a * t^2

Since the initial vertical velocity (v_i) is 0 (since the water is fired horizontally), the equation simplifies to:

d = (1/2) * a * t^2

We know that the initial vertical position (d) is 10.0 m, and the acceleration due to gravity (a) is -9.8 m/s^2 (because gravity pulls downwards). So, let's plug in the values:

10.0 = (1/2) * (-9.8) * t^2

Now we can solve for t:

t^2 = (10.0 * 2) / (-9.8)

t^2 = 2.04

t ≈ √2.04 ≈ 1.43 seconds

So, it takes approximately 1.43 seconds for the water to reach the ground.

b. Now let's find the horizontal distance traveled by the water. We can use the equation for horizontal motion:

d = v * t

We know that the initial horizontal velocity (v) is 15.0 m/s, and the time (t) is 1.43 seconds (as calculated before). Let's substitute these values:

d = 15.0 * 1.43

d ≈ 21.45 meters

So, the horizontal distance traveled by the water is approximately 21.45 meters. Keep an umbrella handy if you don't want to get wet!

To find the time required for the water to reach the ground, we can use the equation of motion:

h = ut + (1/2)gt^2

Where:
h = height (10.0 m)
u = initial velocity (15.0 m/s)
t = time
g = acceleration due to gravity (-9.8 m/s^2)

a. Substituting the given values into the equation, we have:
10.0 = (15.0)t + (1/2)(-9.8)t^2

Simplifying the equation further, we get:
-4.9t^2 + 15.0t - 10.0 = 0

We can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a

For this equation:
a = -4.9, b = 15.0, c = -10.0

Substituting the values into the formula:
t = (-(15.0) ± √((15.0)^2 - 4(-4.9)(-10.0))) / 2(-4.9)

Simplifying further, we get:
t ≈ 2.04 seconds

Therefore, it takes approximately 2.04 seconds for the water to reach the ground.

b. To find the horizontal distance traveled by the water, we can use the formula:
distance = velocity × time

Substituting the given values:
distance = 15.0 m/s × 2.04 s

Calculating further, we get:
distance ≈ 30.6 meters

Therefore, the water travels approximately 30.6 meters horizontally.

To find the time required for the water to reach the ground, we can use the vertical motion equation:

h = ut + (1/2)gt^2

where:
h = height of the nozzle above the ground = 10.0 m
u = initial vertical velocity = 0 m/s (since the water is initially moving horizontally)
g = acceleration due to gravity = 9.8 m/s^2 (assuming Earth's gravity)
t = time

Substituting the given values into the equation:

10.0 = 0t + (1/2)(9.8)t^2

Simplifying the equation:

4.9t^2 = 10.0

Dividing both sides by 4.9:

t^2 = 2.04

Taking the square root of both sides:

t ≈ √2.04

t ≈ 1.43 seconds

Therefore, it would take approximately 1.43 seconds for the water to reach the ground.

To find the horizontal distance traveled by the water, we can use the equation:

d = vt

where:
d = horizontal distance
v = horizontal velocity = 15.0 m/s (given)
t = time = 1.43 seconds (from part a)

Substituting the values into the equation:

d = 15.0 * 1.43

d ≈ 21.45 meters

Therefore, the horizontal distance traveled by the water is approximately 21.45 meters.