Mr. Smith, the high school history teacher (he says that the history of ancient

Question

Mr. Smith, the high school history teacher (he says that the history of ancient Greece is his specialty; the students say that being an all-around twerp is his specialty) has a secret. It’s not much of a secret, but it is, nevertheless, a secret. Mr. Smith owns a small two-story brick house on the outskirts of town. In his back yard are several huge oak trees. One of these trees has a 4-m rope hanging from a high, sturdy branch. (As a matter of fact, the branch is about 4 m from the ground!) On the weekends at around dusk, Mr. Smith likes to dress up in a soldier’s uniform and pretend that he is GI Joe (his middle name is Joseph. . . ). One of GI Joe’s favorite things to do is to run as fast as he can, leap onto the rope, and then see how high he can swing before dropping off the rope and onto the back of an unsuspecting enemy soldier. On one particularly eventful evening, the rope is found to make an angle of about 42 (as measured from the vertically downward direction) when Joe is at his highest point of the swing. How fast was GI Joe running when he leapt onto the rope?

Explanation / Answer

length of the rope l=4m

angle, theta=42 degrees,

by using law of conservation of energy,

1/2*m*v^2=m*g*h

v^2=2g*h

v^2=2g*l(1-cos(theta))

v=sqrt(2g*l(1-cos(theta))

v=sqrt(2*9.8*4(1-cos(42))

==> v=4.487 m/sec

speed v=4.487 m/sec

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