Answer:
The final velocity of the block is 68.85m/s.
Explanation:
The final velocity can be determined by means of the equations for a Uniformly Accelerated Rectilinear Motion:

(1)
But it is necessary to know the acceleration. For a better procedure it will be listed the knowns and unknowns of the problem:
Knowns:
F = 167 N
= 30°
m = 1.75 Kg
d = 23.9 m
= 0.136
Unknowns:
= ?
a = ?
The acceleration can be found by means of Newton's second law:
Where
is the net force, m is the mass and a is the acceleration.
(2)
All the forces can be easily represented in a free body diagram, as it is shown below.
<em>Force in the x axis:</em>
(3)
<em>Forces in the y axis: </em>
(4)
<em>Solving for the forces in the x axis:</em>

Notice that is necessary to found
:
(5)
The normal force can be obtained from equation (4)


The component of the weight in the y axis can be gotten by means of trigonometry:



Remember that the weight is defined as:






The component of the weight in the x axis can be gotten by means of trigonometry:






Then, replacing
and
in equation (3) it is gotten:


Solving for the forces in the y axis:



Replacing the values of
and
in equation (2) it is gotten:




Now that the acceleration is known, equation (1) can be used:

However, since the block was originally at rest its initial velocity will be zero (
).




<u>Hence, the final velocity of the block is 68.85m/s.</u>