Answer:
a. It became deeper by a factor of 3.
Explanation:
What we have is water flowing down a river with constant width. The water slows from speed v to v3 over a shirt distance
Using the equation of continuity
A1V1 = A2V2 ----1
A1 is the area of rectangle
V1 is the velocity of water
Area of rectangle = length x width
We rewrite equation 1 as
λ1w1v1 = λ2w2v2
We have w1 = w2
λ1v1 = λ2v2
λ1*v1 = λ2*v/3
λ1 = λ2/3
So it becomes deeper by a factor of 3
Answer:
Explanation:
ω =
k = 2.5 N/m
m = 10 kg
ω = .5 rad /s
x(t) = A cos(ωt + φ₀)
When t = 0 , x(t) = 0
0 = A cos(ωx 0 + φ₀)
cos φ₀ = 0
φ₀ = π /2
x(t) = A cos(ωt +π /2 )
Putting the value of ω
x(t) = A cos(.5 t +π /2 )
Differentiating on both sides
dx(t)/dt = - .5 A sin(.5 t +π /2 )
v(t) = - .5 A sin(.5 t +π /2 )
Given t =0 , v(t) = -5 m/s
-5 = - .5 A sin(.5 x0 +π /2 )
-5 = - .5 A sinπ /2
A = 10 m
x(t) = 10 cos( .5 t +π /2 )
b )
when t = π ( 3.14 s )
x(t) = - 10 m
when t = 2π ( 6.28s )
x(t) = 0
when t = 3π ( 9.42 s )
x(t) = 10 m
and so on