Answer:
v = 60 m/s
Explanation:
It is given that,
A wave is represented by the equation :
![y=0.2\sin [0.4\pi (x-60)t]](https://tex.z-dn.net/?f=y%3D0.2%5Csin%20%5B0.4%5Cpi%20%28x-60%29t%5D)
We need to find the velocity of the wave
The general equation of a wave is given by :
....(1)
Equation (1) can be written as :
...(2)
If we compare equation (1) and (2) we get :


The velocity of a wave is given by :

So, the velocity of the wave is 60 m/s.
Answer:
D = 43 m
Explanation:
given,
initial velocity = 18 m/s
angle θ = 60°
total horizontal distance covered by the shell is

applying conservation of momentum in horizontal direction
m v₀ cos θ = m₁v₁ + m₂ v₂
m v₀ cos θ = 0.5 m v₂
v₂ = 2 v₀ cos θ.
distance covered by the shell from point of explosion
R' = v t
= 
=
= 
= R
total distance traveled by the shell is
D = 
= 1.5 R
= 
D = 
= 42.9 ≅ 43 m
D = 43 m
Answer:
u = 13.67 m/s
Explanation:
given,
window height = 2 m
window is 7.5 m off the ground on its path up
total distance from the ground to pass the window = 2 + 7.5 = 9.5 m
time taken to go past the window = 1.30 s
using equation of motion



u = 13.67 m/s
hence, the initial velocity of the ball is equal to 13.67 m/s
In electrical circuit, this arrangement is called a R-L series circuit. It is a circuit containing elements of an inductor (L) and a resistor (R). Inductance is expressed in units of Henry while resistance is expressed in units of ohms. The relationship between these values is called the impedance, denoted as Z. Its equation is
Z = √(R^2 + L^2)
Z = √((1.24×10^3 ohms)^2 + (6.95×10^-6 H)^2)
Z = 1,240 ohms
The unit for impedance is also ohms. Since the circuit is in series, the voltage across the inductor and the resistor are additive which is equal to 12 V. Knowing the impedance and the voltage, we can determine the maximum current.
I = V/Z=12/1,240 = 9.68 mA
But since we only want to reach 73.6% of its value, I = 9.68*0.736 = 7.12 mA. Then, the equation for R-L circuits is

, where τ = L/R = 6.95×10^-6/1.24×10^3 = 5.6 x 10^-9
Then,
t = 7.45 nanosecondsPart B.) If t = 1.00τ, then t/τ = 1. Therefore,
I = 6.12 mA