A research group at Dartmouth College has developed a Head Impact Telemetry (HIT) System that can be used to collect data about
1 answer:
Answer:
6.05 cm
Explanation:
The given equation is
2 aₓ(x-x₀)=( Vₓ²-V₀ₓ²)
The initial head velocity V₀ₓ =11 m/s
The final head velocity Vₓ is 0
The accelerationis given by =1000 m/s²
the stopping distance = x-x₀=?
So we can wind the stopping distance by following formula
2 (-1000)(x-x₀)=[]
x-x₀=6.05* m
=6.05 cm
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Answer:
The distance close to the peak is 597.4 m.
Explanation:
Given that,
Distance of the first ship from the mountain
Height of island
Distance of the enemy ship from the mountain
Initial velocity
Angle = 74.9°
We need to calculate the horizontal component of initial velocity
Using formula of horizontal component
Put the value into the formula
We need to calculate the vertical component of initial velocity
Using formula of vertical component
Put the value into the formula
We need to calculate the time
Using formula of time
We need to calculate the height of the shell on reaching the mountain
Using equation of motion
Put the value in the equation
We need to calculate the distance close to the peak
Using formula of distance
Put the value into the formula
Hence, The distance close to the peak is 597.4 m.
Answer:
a)
b)
c)
d)
e)
Explanation:
1) Important concepts
Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".
2) Part a
The equation that describes the simple armonic motion is given by (1)
And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.
For the velocity:
(2)
For the acceleration
(3)
As we can see in equation (3) the acceleration would be maximum when the cosine term would be -1 and on this case:
Since we know the amplitude A=0.002m we can solve for like this:
And we with this value we can find the period with the following formula
3) Part b
From equation (2) we see that the maximum velocity occurs when the sine function is euqal to -1 and on this case we have that:
4) Part c
In order to find the total mechanical energy of the oscillator we can use this formula:
5) Part d
When we want to find the force from the 2nd Law of Newton we know that F=ma.
At the maximum displacement we know that X=A, and in order to that happens , and we also know that the maximum acceleration is given by::
So then we have that:
And since we have everything we can find the force
6) Part e
When the mass it's at the half of it's maximum displacement the term and on this case the acceleration would be given by;
And the force would be given by:
And replacing we have: