The given situation below describes a standing wave because the string is fixed at both ends. A standing wave having three anti-nodes will have a wavelength that is two-thirds the length of the string. After getting the wavelength, this can be multiplied with the frequency to get the wave speed.
For this problem:
wave length = (2/3)(length of string: 68 cm)
wave length = (10/3 cm)
wave speed = wave length x frequency
wave speed = (10/3 cm) x (180 Hz)
wave speed = 600 cm/s or 0.6 m/s
Answer:
(B) (length)/(time³)
Explanation
The equation x = ½ at² + bt³ has to be dimensionally correct. In other words the term bt³ and ½ at² must have units of change of position = length.
We solve in order to find the dimension of b:
[x]=[b]*[t]³
length=[b]*time³
[b]=length/time³
I believe it would be 1.6 East
Fortunately, 'force' is a vector. So if you know the strength and direction
of each force, you can easily addum up and find the 'resultant' (net) force.
When we talk in vectors, one newton forward is the negative of
one newton backward. Hold that thought, while I slog through
the complete solution of the problem.
(100 N forward) plus (50 N backward)
= (100 N forward) minus (50 N forward)
= 50 N forward .
That's it.
Is there any part of the solution that's not clear ?
The solution for this problem is:
r = [(2.90 + 0.0900t²) i - 0.0150t³ j] m/s²
this is for t in seconds and r in meters
v = dr/dt = [0.180t i - 0.0450t² j] m/s²
tan(-36.0º) = -0.0450t² / 0.180t
0.7265 = 0.25t
t = 2.91 s is the velocity vector of the insect
