A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s. What is his wavelength at this speed if his mass is 84.5 kg?
They throw in 24m/h to confuse you. The speed is 100m/9.3s.
Use the formula:
wavelength= Planck’s Constant/(mass x velocity)
Wavelength = 6.63 x 10^-34/ 84.5(100/9.3)
Answer= 7.29 x 10^-37
To determine the wavelength of the sprinter, we'll use the formula:
wavelength = velocity / frequency
First, we need to find the frequency of the sprinter's motion. Frequency is calculated by dividing the speed by the distance:
frequency = speed / distance
The distance is given as 100 m, and the time is given as 9.30 s. Calculating the frequency:
frequency = 100 m / 9.30 s
Next, we know that the velocity of the sprinter is 24.0 mi/h. To convert this to m/s, we can use the conversion factor: 1 mi/h = 0.447 m/s.
velocity = 24.0 mi/h * 0.447 m/s
Now we can substitute the values into the formula:
wavelength = (24.0 mi/h * 0.447 m/s) / (100 m / 9.30 s)
Simplifying the equation:
wavelength = (10.728 m/s) / (10.75 Hz)
Finally, we can calculate the wavelength:
wavelength = 1.001 m
Therefore, the sprinter's wavelength at this speed is approximately 1.001 meters.
To find the wavelength of the sprinter, we need to use the formula:
wavelength = speed / frequency = speed / (1 / time)
First, let's convert the speed from miles per hour to meters per second, since the SI unit for frequency is Hz (1/s) and the SI unit for speed is meters per second.
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, to convert 24.0 mi/h to meters per second:
24.0 mi/h = 24.0 * 1609.34 meters / 3600 seconds = 10.72 m/s
Now, let's find the frequency:
frequency = 1 / time = 1 / 9.30 s = 0.107 Hz
Finally, we can find the wavelength:
wavelength = speed / frequency = 10.72 m/s / 0.107 Hz = 100.00 m
Therefore, the sprinter's wavelength at this speed is 100.00 meters.
The DeBroglie wavelength is
lambda=plancks constant/momentum
covert 24miles/hr to m/s first.