Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te
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Answer:
v = 15.8 m/s
Explanation:
Let's analyze the situation a little, we have a compressed spring so it has an elastic energy that will become part kinetic energy and a potential part for the man to get out of the barrel, in addition there is a friction force that they perform work against the movement. So the variation of mechanical energy is equal to the work of the fictional force
= ΔEm =
-Em₀
Let's write the mechanical energy at each point
Initial
Em₀ = Ke = ½ k x²
Final
= K + U = ½ m v² + mg y
Let's use Hooke's law to find compression
F = - k x
x = -F / k
x = 4400/1100
x = - 4 m
Let's write the energy equation
fr d = ½ m v² + mgy - ½ k x²
Let's clear the speed
v² = (fr d + ½ kx² - mg y) 2 / m
v² = (40 4.00 + ½ 1100 4² - 60.0 9.8 2.50) 2/60.0
v² = (160 + 8800 - 1470) / 30
v = √ (229.66)
v = 15.8 m/s
When acceleration is constant, the average velocity is given by
where and
are the final and initial velocities, respectively. By definition, we also have that the average velocity is given by
where are the final/initial displacements, and
are the final/initial times, respectively.
Take the car's starting position to be at . Then
So we have
You also could have first found the acceleration using the equation
then solve for via
but that would have involved a bit more work, and it turns out we didn't need to know the precise value of anyway.