A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at 60 ° above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at 20 ° to the horizontal. Relative to the coordinate system shown in the figure, the equation of this straight y = ( tan 20 ° ) x − 109 . Where on the hill does the projectile land?
A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at 60 ° above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at 20 ° to the horizontal. Relative to the coordinate system shown in the figure, the equation of this straight y = ( tan 20 ° ) x − 109 . Where on the hill does the projectile land?
A projectile is shot at a hill, the base of which is 300 m away. The projectile is shot at
60
°
above the horizontal with an initial speed of 75 m/s. The hill can be approximated by a plane sloped at
20
°
to the horizontal. Relative to the coordinate system shown in the figure, the equation of this straight
y
=
(
tan
20
°
)
x
−
109
. Where on the hill does the projectile land?
A bungee jumper plans to bungee jump from a bridge 64.0 m above the ground. He plans to use a uniform elastic cord, tied to a harness around his body, to stop his fall at a point 6.00 m above the water. Model his body as a particle and the cord as having negligible mass and obeying
Hooke's law. In a preliminary test he finds that when hanging at rest from a 5.00 m length of the cord, his body weight stretches it by 1.55 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the bridge.
(a) What length of cord should he use?
Use subscripts 1 and 2 respectively to represent the 5.00 m test length and the actual jump length. Use Hooke's law F = KAL and the fact that the change in length AL for a given force is proportional the length L (AL = CL), to determine the force constant for the test case and for the
jump case. Use conservation of mechanical energy to determine the length of the rope. m
(b) What maximum acceleration will he…
210. Sometimes the Helmholtz free energy F(T, V, N) divided by temperature, T, is an interesting
quantity. For example, the quantity is proportional to the logarithm of the equilibrium constant or
solubilities.
A. Derive a relationship showing that
Find the constant of proportionality.
a
F
αυ
ƏT T
B. Suppose F(T) depends on temperature in the following way:
F(T)=2aT²+bT.
Find S(T) and U(T).
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