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
The power dissipated across a component can be calculated through the formula P=I^2xR
Substituting the values in we get P=(0.5)^2x10=2.5W
Given the equation for the Speed of a Satellite
v = SqRt{Gravitational Constant}{Mass of Earth} divided by the radius given in your problem
we have:
(square root whole term on right side)
v = G Me
———
r
so. (6.67x10^-11)(5.97x10^24)
___________________
(8.0x10^6)
v = 7055 m/s (which is reasonable)
so utilize the Kinetic Energy Formula
KE = 1/2mv^2
KE = 1/2(200)(7055)^2
KE = 4.977x10^9 J
You are correct earth science is studied to predict planetery changes