Classical Mechanics
Classical Mechanics
5th Edition
ISBN: 9781891389221
Author: John R. Taylor
Publisher: University Science Books
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Chapter 10, Problem 10.1P
To determine

Show that the result of mαr'α=0.

Expert Solution & Answer
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Answer to Problem 10.1P

The result of mαr'α=0 is shown here.

Explanation of Solution

Write the expression for the position of the CM ,

    rα=R+r'α        (I)

Here, rα is the position of the CM, R is the position relative to the origin O and rα' is the position.

Rewrite the above equation,

    rα'=rαR        (II)

Write the expression for the force,

    αmαrα'=0        (III)

Here, mα is the mass of the object.

Substitute (III) in (II),

    αmα(rαR)=0αmαrααmαR=0MMαmαrαRαmα=0        (IV)

Substitute 1Mαmαrα for R in the above equation,

    αmαrα'=MRRM=0        (V)

Therefore, the result of mαr'α=0 is shown here.

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In a naval battle, a battleship is attempting to fire on a destroyer. The battleship is a distance d1 = 2,150 m to the east of the peak of a mountain on an island, as shown in the figure below. The destroyer is attempting to evade cannon shells fired from the battleship by hiding on the west side of the island. The initial speed of the shells that the battleship fires is vi = 245 m/s. The peak of the mountain is h = 1,840 m above sea level, and the western shore of the island is a horizontal distance d2 = 250 m from the peak. What are the distances (in m), as measured from the western shore of the island, at which the destroyer will be safe from fire from the battleship? (Note the figure is not to scale. You may assume that the height and width of the destroyer are small compared to d1 and h.)
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