Which of the following is not a mechanical form of energy?
1 answer:
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Answer:
757,93 feets
Explanation:
We can make a right triangle between the boat (A), the Coast Guard officer (B) and the base of the observation tower (C), like in the graph attached. Now, you could also made a rectangle, adding the horizontal at the height of the Coast Guard, starting in B and ending in D, the vertex opossing C.
The angle of depression, its O in the graph.
Now, as we got an rectangle, of course, the segment AD its the same length as CB, and CA, the distance from the boat to shoreline, its the same length as DB.
ADB its an right triangle, with AB, the hypothenuse, and BD and DA, the catheti (or <em>legs</em>).
Now, we know the lenght BC, the height of the tower, 53 feets, so we also know the lenght of DA. DA its the opposite cathetus to the angle O. We wish to know the length AC, equal to the lenght DB, the adjacent cathetus of the angle O.
Know, the trigonometric function that connects the adjacent cathetus with the opossite cathetus its the tangent.
We can take that the angle O = 4 °, and knowing that the opossite cathetus its 53 feets, we got:
This its equal to the distance from the boat to the shoreline.
The horizontal distance covered by the ball before hitting the water is 70.4 m
Explanation:
The motion of the ball is the motion of a projectile, so it consists of two independent motions:
- A uniform motion along the horizontal (x) direction
- A uniformly accelerated motion along the vertical (y) direction
We start by calculating the time of flight of the ball. This can be done by analyzing the vertical motion. We can use the following suvat equation:
where:
s = -16.5 m is the vertical displacement of the ball (it is negative because we take upward as positive direction)
is the initial vertical velocity of the ball, which is given by
where
u = 23.5 m/s is the initial velocity
is the angle of projection
Substituting,
is the acceleration of gravity, downward
Substituting everything into the equation we get:
Solving the equation for t, we find the time of flight of the ball:
t = -0.94 s
t = 3.59 s
We ignore the 1st solution since it is negative, so the ball reaches the water after 3.59 seconds.
Now we analyze the horizontal motion of the ball. The horizontal velocity is constant and it is:
Therefore, the horizontal distance covered in a time t is
And substituting t = 3.59 s, we find
So, the horizontal distance covered by the ball before hitting the water is 70.4 m.
Learn more about projectile motion:
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