Estimate the speed in mph with which water comes out of a garden hose using your past observations of water coming out of garden hoses and your knowledge of projectile motion. (Take the inclination angle to be 45°, the initial height to be 1.0 m, and the range of the stream to be 4 m.)
Range = Vo^2*sin(2A)/g = 4 m.
Vo^2*sin(90)/9.8 = 4.
0.102Vo^2 = 4.
Vo^2 = 39.2.
Vo = 6.3 m/s. * 1mi/1600m * 3600s/h =
14.1 mi/h.
To estimate the speed in mph with which water comes out of a garden hose, we can use the principles of projectile motion.
First, let's calculate the initial velocity of the water stream. We know that the range, which is the horizontal distance covered, is 4 meters. In projectile motion, the range is related to the initial velocity and the angle of inclination.
The formula for the range (R) is given by R = (v^2 * sin(2θ)) / g, where v is the initial velocity, θ is the angle of inclination, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
We can rearrange this equation to solve for the initial velocity (v):
v = sqrt((R * g) / sin(2θ))
Plugging in the values for the range (4 m), angle of inclination (45°), and acceleration due to gravity (9.8 m/s^2), we get:
v = sqrt((4 * 9.8) / sin(2 * 45°))
v = sqrt(39.2 / 1)
v = 6.26 m/s
Now, to convert this velocity from meters per second (m/s) to miles per hour (mph), we need to use the conversion factor:
1 m/s = 2.237 mph
So, the velocity in mph would be:
v_mph = 6.26 * 2.237
v_mph = 13.97 mph (rounded to two decimal places)
Therefore, based on the given parameters, the estimated speed at which water comes out of the garden hose is approximately 13.97 mph.