A skateboarder shoots off a ramp with a velocity of 7.3 m/s, directed at an angle of 60° above the horizontal. The end of the ra
1 answer:
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1) Maximum
2) Maximum
Explanation:
The force acting on a mass on a spring is given by Hooke's law; in magnitude:
where
F is the force
k is the spring constant
x is the displacement
Also we know from Newton's second law that we can write
where
m is the mass
a is the acceleration
So we can write the equation as
(1)
From this relationship, we see that the acceleration is directly proportional to the displacement.
On the other hand, we know that the total mechanical energy of the system mass-spring is constant, and it is given by
(2)
where the first term is the elastic potential energy while the second term is the kinetic energy, and where
v is the velocity of the mass
From eq. (2), it is clear that when displacement increases, velocity decreases, and vice-versa; however, from eq.(1) we also know that acceleration is proportional to the displacement.
Therefore this means that:
- When acceleration increases, velocity decreases
- When acceleration decreases, velocity increases
Therefore, the two answers here are:
- When the acceleration of a mass on a spring is zero, the velocity is at a maximum
When the velocity of a mass on a spring is zero, the acceleration is at a maximum
Answer:
The resultant velocity is 86.1 mi/h.
Explanation:
The law of cosines is given by:
Where:
c: is the resultant velocity =?
a: is the velocity of the plane = 75.0 mi/h
b: is the velocity of the wind = 15.0 mi/h
θ: is the angle between "a" and "b"
The angle between "a" and "b" can be found as follows:
Now, by using the law of cosines we have:
Therefore, the resultant velocity is 86.1 mi/h.
The law of sines is:
Where:
γ: is the angle between "b" and "c"
α: is the angle between "a" and "c"
So, if we want to find "c" by using the law of sines, we need to know another angle besides θ (γ or α), and the statement does not give us.
I hope it helps you!