A drunken sailor stumbles 550 meters north, 500 meters northeast, then 450 meters northwest. What is the total displacement and
1 answer:
Answer:
Resultant displacement = 1222.3 m
Angle is 88.3 degree from +X axis.
Explanation:
A = 550 m north
B = 500 m north east
C = 450 m north west
Write in the vector form
A = 550 j
B = 500 (cos 45 i + sin 45 j ) = 353.6 i + 353.6 j
C = 450 ( - cos 45 i + sin 45 j ) = - 318.2 i + 318.2 j
Net displacement is given by
R = (353.6 - 318.2) i + (550 + 353.6 + 318.2) j
R = 35.4 i + 1221.8 j
The magnitude is
The direction is given by
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Answer:
the maximum is I₁ axis of rotation at the end
the minimum moment is I₂ axis of rotation at the center of mass
Explanation:
For this exercise we use the definition moment of inertia
I = ∫ r² dm
for bodies of high symmetry it is tabulated; In this case we can approximate a broomstick to a thin rod, the moment of inertia with respect to a perpendicular axis when varying are
at one end
I₁ = ⅓ mL²
in in center
I₂ = m L²
There is another possible axis of rotation around the axis of the broom, in this case we have a solid cylinder
I₃ = m r²
remember that the diameter of the broom is much smaller than its length, therefore this moment of inertia is very small
when examining the different moments of inertia:
the maximum is I₁ axis of rotation at the end
the minimum moment is I₂ axis of rotation at the center of mass
Explanation:
It is given that,
Height of the building, h = 44 m
Initial horizontal velocity,
Initial vertical velocity,
It can be assumed to find the maximum height of the projectile and time taken to reach the maximum height.
The formula for the maximum height is given by :
g is the acceleration due to gravity
The total maximum height, h' = h + H
The formula for the time of flight is given by :
Hence, this is the required solution.