Answer: -2.25 ft/s
Explanation:
we have the following parameters
length of the ladder = 10 ft
distance of the base of the ladder (x) = 6 ft
applying Pythagoras theorem
X^2 + Y^2 = 10^2 ............equation 1
X^2 + Y^2 = 100
differentiating the above we have
2X (dx/dt) + 2Y (dy/dt) = 0 ...........equation 2
substituting the value of X into equation 1
6^2 + Y^2 = 10^2
Y^2 = 100 - 36
Y =
Y = 8
now that we have Y= 8, X = 6 and dx/dt (rate of sliding of the base) = 3 ft/s, we can substitute them into equation 2 to get dy/dt (rate of sliding of the top)
we now have
(2 x 6 x 3 ) + (2 x 8 x dy/dt ) = 0
36 + 16(dy/dt) = 0\
dy/dt = (-36) / 16
= -2.25 ft/s ( - means its sliding down)
Answer:
The value is
Explanation:
From the question we are told that
The focal length of the objective is
The focal length of the eyepiece is
The tube length is
Generally the magnitude of the overall magnification is mathematically represented as
Where is the objective magnification which is mathematically represented as
=>
=>
is the eyepiece magnification which is mathematically evaluated as
So
Answer:
Explanation:
An object is at rest along a slope if the net force acting on it is zero. The equation of the forces along the direction parallel to the slope is:
(1)
where
is the component of the weight parallel to the slope, with m being the mass of the object, g the acceleration of gravity,
the angle of the slope
is the frictional force, with
being the coefficient of friction and R the normal reaction of the incline
The equation of the forces along the direction perpendicular to the slope is
where
R is the normal reaction
is the component of the weight perpendicular to the slope
Solving for R,
And substituting into (1)
Re-arranging the equation,
This the condition at which the equilibrium holds: when the tangent of the angle becomes larger than the value of , the force of friction is no longer able to balance the component of the weight parallel to the slope, and so the object starts sliding down.
Answer:
42 m/s
Explanation:
by definition of the velocity(speed) of a wave,
The velocity of light, v, is the product of its wavelength, λ , and its frequency, f.
V= fλ
frequency - number of occurances in a unit time
(check the graph)
