Please tell me if if these statements are true or false
2 answers:
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Before the engines fail, the rocket's altitude at time <em>t</em> is given by
and its velocity is
The rocket then reaches an altitude of 1150 m at time <em>t</em> such that
Solve for <em>t</em> to find this time to be
At this time, the rocket attains a velocity of
When it's in freefall, the rocket's altitude is given by
where is the acceleration due to gravity, and its velocity is
(a) After the first 11.2 s of flight, the rocket is in the air for as long as it takes for to reach 0:
So the rocket is in motion for a total of 11.2 s + 32.6 s = 43.4 s.
(b) Recall that
where and
denote final and initial velocities, respecitively,
denotes acceleration, and
the difference in altitudes over some time interval. At its maximum height, the rocket has zero velocity. After the engines fail, the rocket will keep moving upward for a little while before it starts to fall to the ground, which means
will contain the information we need to find the maximum height.
Solve for and we find that the rocket reaches a maximum altitude of about 1930 m.
(c) In part (a), we found the time it takes for the rocket to hit the ground (relative to ) to be about 32.6 s. Plug this into
to find the velocity before it crashes:
That is, the rocket has a velocity of 196 m/s in the downward direction as it hits the ground.
a) See free-body diagram in attachment
b) The book is stationary in the vertical direction
c) The net horizontal force is 35 N in the forward direction
d) The net force on the book is 35 N in the forward horizontal direction
e) The acceleration is in the forward direction
Explanation:
a)
The free-body diagram of a body represents all the forces acting on the body using arrows, where the length of each arrow is proportional to the magnitude of the force and points in the same direction.
From the diagram of this book, we see there are 4 forces acting on the book:
- The applied force, F = 50 N, pushing forward in the horizontal direction
- The frictional force, , pulling backward in the horizontal direction (the frictional force always acts in the direction opposite to the motion)
- The weight of the book, , where m is the mass of the book and
is the acceleration of gravity, acting downward. We can calculate its magnitude using the mass of the book, m = 4 kg:
- The normal reaction exerted by the desk on the book, N, acting upward, and balancing the weight of the book
b)
The book is in equilibrium in the vertical direction, therefore there is no motion.
In fact, the magnitude of the normal reaction (N) exerted by the desk on the book is exactly equal to the weight of the book (W), so the equation of motion along the vertical direction is
where a is the acceleration; however, since N = W, this becomes
And since the book is initially at rest on the desk, this means that there is no motion.
c)
We said there are two forces acting in the horizontal direction:
- The applied force, F = 50 N, forward
- The frictional force, , backward
Since they act along the same line, we can calculate their resultant as
and therefore the net force is 35 N in the forward direction.
d)
The net force is obtained as the resultant of the net forces in the horizontal and vertical direction. However, we have:
- The net force in the horizontal direction is 35 N
- The net force in the vertical direction is zero, because the weight is balanced by the normal reaction
Therefore, this means that the total net force acting on the book is just the net force acting on the horizontal direction, so 35 N forward.
e)
The acceleration of the book can be calculated by using Newton's second law:
where
is the net force
m is the mass
a is the acceleration
Here we have:
(in the forward direction)
m = 4 kg
Therefore, the acceleration is
(forward)
Learn more about forces, weight and Newton's second law:
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