Answer:
7.875 ft/s
Explanation:
L = 15 ft
dx/dt = 3 ft/s
x = 9 ft
Let the top of ladder is coming down with the rate of dy/dt.
use Pythagorean theorem
L^2 = x^2 + y^2 .... (1)
Differentiate both sides with respect to t
0 = 2 x dx/dt + 2y dy/dt
x dx/dt = - y dy/dt
When, x = 9 ft then y = ? . Put this in equation (1)
15^2 = 9^2 + y^2
225 - 81 = y^2
y = 12 ft
So
dy/dt = - x (dx/dt) / y = - 9 (3) / 12 = - 9/4 ft/s
Let A be the area of the triangle
A = 1/2 (base)(height)
A = 1/2 (x y)
Differentiate both sides with respect to t
dA/dt = 0.5 (y dx/dt + x dy/dt)
dA/dt = 0.5 [ 12 (3) - 9 (9/4)]
dA/dt = 0.5(36 - 81 /4) = 31.5 / 4 = 7.875 ft/s
If a person returns to the position he started again. like moving in a circle track
Answer:
Kinematics is the branch of classical mechanics that describes the motion of points, objects and systems of groups of objects, without reference to the causes of motion (i.e., forces ). The study of kinematics is often referred to as the “geometry of motion.”
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Answer: Length axis f= 114.3 Hz, Width axis f=228.67 Hz
Explanation:
We are given that,
Length of tub= 1.5 m
Width of tub= 0.75 m
Sound speed= 343 m/s
Now, we are also given shower is closed.
So, frequency is given as:
f=
For length axis
Put v= 343 m/s, m=1 and L=1.5 m
f= 1 *
f= 114.3 Hz
For next resonant frequency, m=2
f= 2*
f= 228.67
For width axis
Put v= 343 m/s, m=1 and L= 0.75 m
f= 1*
f= 228.67 Hz
For next frequency, m=2
f= 2*
f= 457.34 Hz