Max height occurs when v = 0.
v(t) = ds(t)/dt
v(t) = 80 - 32t
0 = 80 - 32t
t = 5/2
s(5/2) = 80(5/2) - 16(5/2)^2
s(5/2) = 100
Answer: 100 ft
96 = 80t - 16t²
t = 3, 2
(80 ± √256) / 32 using the quadratic equation.
v(2) = 16
v(3) = -16
The speed at which sound travels through the gas in the tube is 719.94m/s
<u>Explanation:</u>
Given:
Frequency, f = 11999Hz
Wavelength, λ = 0.03m
Velocity, v = ?
Sound speed in the tube is calculated by multiplying the frequency v by the wavelength λ.
As the sound loudness changed from a maximum to a minimum, then we know the sound interference in the case changed from constructive interference (the two sound waves are in phase, i.e. peaks are in a line with peaks and so the troughs), to a destructive interference (peaks coinciding with troughs). The least distance change required to cause such a change is a half wavelength distance, so:
λ/2 = 0.03/2
λ = 0.06m
We know,
v = λf
v = 0.06 X 11999Hz
v = 719.94m/s
Therefore, the speed at which sound travels through the gas in the tube is 719.94m/s
We are given the equation:
<span>x = 11t^2
</span>
We use that equation to calculate for the distance traveled.
For (a)
At t=2.20 sec,
x =53.24 meters
At t=2.95 sec,
x =95.73 meters
Velocity = (95.73 meters - 53.24<span> meters) / (2.95 s - 2.20 s ) = 56.65 m/s
</span>For (b)
At t=2.20 sec,
x =53.24 meters
At t=2.40 sec,
x =63.36 meters
Velocity = (63.36 meters - 53.24<span> meters) / (2.40 s - 2.20 s ) = 50.6 m/s</span>
Speed = distance / time
If you input your numbers into this equation you will be able to find the cyclists average speed
