Answer:
a)Amplitude ,A = 2 mm
b)f=95.49 Hz
c)V= 30 m/s ( + x direction )
d) λ = 0.31 m
e)Umax= 1.2 m/s
Explanation:
Given that
![y=2\ mm\ sin[(20m^{-1})x-(600s^{-1})t]](https://tex.z-dn.net/?f=y%3D2%5C%20mm%5C%20sin%5B%2820m%5E%7B-1%7D%29x-%28600s%5E%7B-1%7D%29t%5D)
As we know that standard form of wave equation given as

A= Amplitude
ω=Frequency (rad /s)
t=Time
Φ = Phase difference
![y=2\ mm\ sin[(20m^{-1})x-(600s^{-1})t]](https://tex.z-dn.net/?f=y%3D2%5C%20mm%5C%20sin%5B%2820m%5E%7B-1%7D%29x-%28600s%5E%7B-1%7D%29t%5D)
So from above equation we can say that
Amplitude ,A = 2 mm
Frequency ,ω= 600 rad/s (2πf=ω)
ω= 2πf
f= ω /2π
f= 300/π = 95.49 Hz
K= 20 rad/m
So velocity,V
V= ω /K
V= 600 /20 = 30 m/s ( + x direction )
V = f λ
30 = 95.49 x λ
λ = 0.31 m
We know that speed is the rate of displacement

![U=2\ mm\ sin[(20m^{-1})x-(600s^{-1})t]](https://tex.z-dn.net/?f=U%3D2%5C%20mm%5C%20sin%5B%2820m%5E%7B-1%7D%29x-%28600s%5E%7B-1%7D%29t%5D)
![U=1200\ cos[(20m^{-1})x-(600s^{-1})t]\ mm/s](https://tex.z-dn.net/?f=U%3D1200%5C%20cos%5B%2820m%5E%7B-1%7D%29x-%28600s%5E%7B-1%7D%29t%5D%5C%20mm%2Fs)
The maximum velocity
Umax = 1200 mm/s
Umax= 1.2 m/s
-- The vertical component of the ball's velocity is 14 sin(<span>51°) = 10.88 m/s
-- The acceleration of gravity is 9.8 m/s².
-- The ball rises for 10.88/9.8 seconds, then stops rising, and drops for the
same amount of time before it hits the ground.
-- Altogether, the ball is in the air for (2 x 10.88)/(9.8) = 2.22 seconds
==================================
-- The horizontal component of the ball's velocity is 14 cos(</span><span>51°) = 8.81 m/s
-- At this speed, it covers a horizontal distance of (8.81) x (2.22) = <em><u>19.56 meters</u></em>
before it hits the ground.
As usual when we're discussing this stuff, we completely ignore air resistance.
</span>
B
Assume north and east as two sides of a right angled triangle. magnitude of the distance is then given by the length of the hypotenuse which is 
where a = 1.2 km north
and b = 1.6 km east
magnitude = 2 km
Direction is given by the angle between them, that is atan(a/b) = 36.86 deg north of east = 53.1 deg east of north.
Answer: K.E = 0.4 J
Explanation:
Given that:
M = 1.0 kg
h = 0.04 m
K.E = ?
According to conservative of energy
K.E = P.E
K.E = mgh
K.E = 1 × 9.81 × 0.04
K.E = 0.3924 Joule
The kinetic energy of the pendulum at the lowest point is 0.39 Joule