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    Derivatives : Velocity and Displacement

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    27. A ball is thrown straight downward from the top of a tall building. The initial speed of the ball is 10 m/s. It strikes the ground with a speed of 60 m/s. How tall is the building?

    Answer: y0 = 178.57 m

    35. A stone is dropped from rest at an initial height h above the surface of the Earth. Show that the speed with which it strikes the ground is v = √2gh.

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    27. A ball is thrown straight downward from the top of a tall building. The initial speed of the ball is 10 m/s. It strikes the ground with a speed of 60 m/s. How tall is the building?

    Answer: y0 = 178.57 m

    Solution. Assume that the height of the building is h meters. Denote by H(t) the height of a ball at time t. Note that the derivative of H(t) with respect to t is the speed; and the second derivative of H(t) is the acceleration of this ball, i.e., . Assume that the mass of a ball is M.

    By the Newton's 3rd law, we have

    i.e.,

    Obviously, when t=0, H(0)=h and H'(0)=-10.

    Note 1: H'(0) is the initial speed of the ball, so by given information, H'(0)= -10 (m/s)

    NOTE 2: Why do we use -10 m/s? This is the direction of the ball is downwards!

    So, we set up the ...

    Solution Summary

    Derivatives are applied to velocity and displacement. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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