#1
initial height = 25000 ft
as we know that
1 ft = 0.3048 m
so we have
H = 25000(0.3048) = 7620 m
#2
If mass of the man = 90 kg
now the initial potential energy is given as
[tex]U = mgh[/tex]
[tex]U = (90)(9.8)(7620)[/tex]
[tex]U = 6.72 \times 10^6 J[/tex]
#3
Gravitational force that is acting on it is given by
[tex]F = mg[/tex]
[tex]F = 90(9.8) = 882 N[/tex]
so this is the force by which earth is attracting him towards it as we can see due to this force the man is accelerating towards the earth
#4
As we know that gravitational force is given by
[tex]F = \frac{GMm}{r^2}[/tex]
here we know that
r = R + h
R = radius of earth ([tex]6.37 \times 10^6 m[/tex])
h = 7620 m
now we have acceleration at that point is
[tex]a = \frac{F}{m}[/tex]
[tex]a = \frac{GM}{r^2}[/tex]
[tex]a = \frac{(6.67\times 10^{-11})(5.98 \times 10^{24})}{(6.37 \times 10^6 + 7620)^}[/tex]
[tex]a = 9.806 m/s^2[/tex]
#5
by energy conservation we have
[tex]KE = PE[/tex]
[tex]\frac{1}{2}mv^2 = mgh[/tex]
[tex]v^2 = 2gh[/tex]
[tex]v^2 = 2(9.8)(7620)[/tex]
[tex]v = 386.5 m/s[/tex]
#6
final speed due to wind resistance is 150 mph
now we know that
1 mile = 1609 meter
so this speed in m/s is given as
[tex]150 mph = 150(\frac{1609 m}{3600 s})[/tex]
[tex]v = 67 m/s[/tex]
#7
No Luke is not accelerating when his speed is 150 mph
because at this speed his velocity will become constant
and since there is no change in velocity so his acceleration will become zero
#8
since at 150 mph the acceleration of Luke is zero
so net force on him must be zero
so we will have
wind force = weight or force due to earth
[tex]F_{wind} = 882 N[/tex]
#9
If there is no wind resistance then there will be energy conservation
so KE = PE
[tex]KE = 6.72 \times 10^6 J[/tex]
#10
Net will reduce the velocity of luke to be zero by taking long time
As we know that force on a system is given by
[tex]F = \frac{\Delta P}{\Delta t}[/tex]
so if we increase the time interval here then we will have less force
so Luke will unhurt due to more time to decrease his speed to be zero
