Answer:


Explanation:
Force of friction on M mass so that it will move down the inclined plane is given as

now if it is moving down the inclined plane at constant speed
so we will have

on other side the mass "m" will go up at constant speed
so we have

so we have

so we have

for special case when m = M
then we have

Define
v = volume of a drop per second, cm³/s
The time taken to fill 200 cm³ is 1 hour.
Let V = 200 cm³, the filled volume.
Let t = 1 h = 3600 s, the time required to fill the volume.
Therefore,

The average volume of a single drop is approximately 0.0556 cm³.
Answer: 0.0556 cm³
Answer:
distance between object and image = 18.9 cm
Explanation:
given data
radius of curvature = 18 cm
focal length = 1/2 radius of curvature
magnification = 40%
to find out
distance between object and image
solution
we know lens formula that is
1/f = 1/v + 1/u ....................1
here f = 18 /2 and v and u is object and image distance
and we know m = 40% = 0.40
so 0.40 = -v / u
so here v = - 0.40 u
so from equation 1
1/f = 1/v + 1/u
2/18 = - 1/0.40u + 1/u
u = -13.5 cm ..................2
and
v = -0.40 (- 13.5)
v = 5.4 cm ......................3
so from equation 2 and 3
distance between object and image = 5.4 + 13.5
distance between object and image = 18.9 cm
Before the engines fail
, the rocket's horizontal and vertical position in the air are


and its velocity vector has components


After
, its position is


and the rocket's velocity vector has horizontal and vertical components


After the engine failure
, the rocket is in freefall and its position is given by


and its velocity vector's components are


where we take
.
a. The maximum altitude occurs at the point during which
:

At this point, the rocket has an altitude of

b. The rocket will eventually fall to the ground at some point after its engines fail. We solve
for
, then add 3 seconds to this time:

So the rocket stays in the air for a total of
.
c. After the engine failure, the rocket traveled for about 34.6 seconds, so we evalute
for this time
:
