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Answer:
ΔU = -70 J
Explanation:
ΔU = Q − W
where ΔU is the change in internal energy,
Q is the heat absorbed by the system,
and W is the work done by the system (on the surroundings).
30 J of thermal energy is released, so Q = -30 J.
40 J of work is done by the system, so W = 40 J.
Therefore, the change in internal energy is:
ΔU = -30 J − 40 J
ΔU = -70 J
Answer:
Explanation:
V = 100sin(ωt) + 150cos(ωt)
let x = ωt
V = 100sin(x) + 150cos(x)
a maximum or minimum will occur when the derivative is zero
V' = 100cos(x) - 150sin(x)
0 = 100cos(x) - 150sin(x)
100cos(x) = 150sin(x)
100/150 = sin(x)/cos(x)
0.6667 = tan(x)
x = 0.588 rad
V = 100sin(0.588) + 150cos(0.588)
V = 180.27756
as the maximum will not occur until ωt = 0.588 radians, for a cosine function we subtract that amount as a phase angle φ
V = 180.3 cos(ωt - 0.588)
or as a sine function, the phase angle lags the cosine by a difference of π/2
V = 180.3sin(ωt - (0.588 - π/2)
V = 180.3sin(ωt + 0.983)
Answer:

Explanation:
The minimum distance for takeoff is:




Answer:v=0.4 m/s
Explanation:
Mass hockey player 
mass of cup 
Velocity of cup 
let v be the velocity of the combined system
Conserving momentum



