A tin can is filled with water to a depth of 50 cm. A hole 16 cm above the bottom of the can produces a stream of water that is directed at an angle of 35degrees above the horizontal.
Find the range of this stream of water.
Find the maximum height of this stream of water.
To find the range of the water stream, we can break down the problem into two parts: the horizontal component of the velocity and the vertical component of the velocity.
First, let's determine the horizontal velocity component. The water stream is directed at an angle of 35 degrees above the horizontal, so we can use trigonometry to find the horizontal velocity component.
horizontal velocity component = initial velocity * cos(angle)
The initial velocity of the water can be calculated using the Torricelli's equation for the velocity of water flowing out of a hole in a container:
initial velocity = sqrt(2 * g * h)
Where g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the depth of water above the hole (50 - 16 = 34 cm = 0.34 m).
Substituting these values into the equation:
initial velocity = sqrt(2 * 9.8 * 0.34) = 2.18 m/s
Now, let's calculate the horizontal velocity component:
horizontal velocity component = 2.18 * cos(35) ≈ 1.79 m/s
Next, let's determine the vertical velocity component. The vertical velocity component is simply the initial velocity multiplied by the sine of the angle.
vertical velocity component = initial velocity * sin(angle)
vertical velocity component = 2.18 * sin(35) ≈ 1.25 m/s
Now, we can use these velocity components to find the range and maximum height of the water stream.
To find the range, we can use the equation:
range = (horizontal velocity component * vertical velocity component) / g
range ≈ (1.79 * 1.25) / 9.8 ≈ 0.228 m
Therefore, the range of the water stream is approximately 0.228 meters.
To find the maximum height, we can use the equation:
maximum height = (vertical velocity component^2) / (2 * g)
maximum height ≈ (1.25^2) / (2 * 9.8) ≈ 0.080 m
Therefore, the maximum height of the water stream is approximately 0.080 meters.