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?
And what was your problem with my response to your first post?
what is the answer?
To find the wavelength at this speed, we can use the formula:
wavelength = velocity / frequency
First, let's find the frequency. The frequency (f) can be calculated using the formula:
frequency = 1 / time
Given that the time (t) is 9.30 seconds, we can calculate the frequency:
frequency = 1 / 9.30 s
frequency ≈ 0.1075 Hz
Now, let's find the velocity. The velocity (v) can be calculated using the formula:
velocity = 24.0 mi/h = 24.0 * 1609.34 m/h (since 1 mile = 1609.34 meters)
velocity ≈ 38624.16 m/h ≈ 10.73 m/s
Finally, let's calculate the wavelength using the formula mentioned earlier:
wavelength = velocity / frequency
wavelength = 10.73 m/s / 0.1075 Hz
wavelength ≈ 99.77 meters
Therefore, the sprinter's wavelength at this speed is approximately 99.77 meters.
To find the wavelength of the sprinter, we need to use the wavelength equation from wave mechanics. However, it's important to note that the wavelength equation is typically used to describe waves, not the motion of objects or people.
The equation for wavelength (λ) is:
λ = v/f
where:
λ is the wavelength in meters (m)
v is the velocity or speed of the wave in meters per second (m/s)
f is the frequency of the wave in hertz (Hz)
In this case, we don't have the frequency of the sprinter, but we have the speed in miles per hour (mi/h). Therefore, we first need to convert the speed from miles per hour to meters per second.
1 mile = 1609.34 meters (approximately)
1 hour = 3600 seconds
So, to convert miles per hour to meters per second, we need to multiply the speed by the conversion factor:
24.0 mi/h * (1609.34 m/1 mi) * (1 h/3600 s) = v m/s
Now, we can substitute the value of v into the wavelength equation to solve for λ. However, since we don't have the frequency (f) of the sprinter, we cannot compute the wavelength accurately with the given information.