Answer:
Explanation:
To solve this problem we use the Momentum's conservation Law, before and after the girl catch the ball:
(1)
At the beginning the girl is stationary:
(2)
If the girl catch the ball, both have the same speed:
(3)
We replace (2) and (3) in (1):
We can now solve the equation for v_{f}:
Answer:
Explanation:
Torque is defined as the cross product between the position vector ( the lever arm vector connecting the origin to the point of force application) and the force vector.
Due to the definition of cross product, the magnitude of the torque is given by:
Where 
is the angle between the force and lever arm vectors. So, the length of the lever arm (r) is minimun when 
is equal to one, solving for r:
<span>We can think this through intuitively. A frequency of 256 Hz means that the wave has 256 cycles each second. If the wavelength is 1.33 meters, then there are 256 of them each second. Therefore, we just need to multiply the wavelength by the frequency to find the speed of sound. (Note that the units Hz = 1 / s)
v = (frequency) x (wavelength)
v = (256 Hz) x (1.33 m)
v = 340.5 m/s
The speed of sound in the vicinity of the fork is 340.5 m/s</span>
Answer:
t=37 mins -> 2220sec
We want "T" which is the pendulum time constant
Using this equation
.5A=Ae^(-t/T)
The .5A is half the amplitude
Take ln of both sides to get ride of Ae
=ln(.5)=-2220/T
Now rearrange to = T
T=-2220/ln(.5) = 3202.78sec / 60 secs = 53.38 mins -> first part of the answer.
The second part is really easy. It took 37 mins to decay half way. meaning to decay another half of 50% which equals 25% it will take an additional 37 mins!
Answer:
W = -510.98J
Explanation:
Force = 43N, 61° SW
Displacement = 12m, 22° NE
Work done is given as:
W = F*d*cosA
where A = angle between force and displacement.
Angle between force and displacement, A = 61 + 90 + 22 = 172°
W = 43 * 12 * cos172
W = -510.98J
The negative sign shows that the work done is in the opposite direction of the force applied to it.
