A ball is dropped from the roof of a 25-m-tall building. What is the velocity of the object when it touches the ground? Suppose
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Answer:
.
Explanation:
The frequency of a wave is equal to the number of wave cycles that go through a point on its path in unit time (where "unit time" is typically equal to one second.)
The wave in this question travels at a speed of . In other words, the wave would have traveled
in each second. Consider a point on the path of this wave. If a peak was initially at that point, in one second that peak would be
How many wave cycles can fit into that ? The wavelength of this wave
gives the length of one wave cycle. Therefore:
.
That is: there are wave cycles in
of this wave.
On the other hand, Because that of this wave goes through that point in each second, that
wave cycles will go through that point in the same amount of time. Hence, the frequency of this wave would be
Because one wave cycle per second is equivalent to one Hertz, the frequency of this wave can be written as:
.
The calculations above can be expressed with the formula:
,
where
represents the speed of this wave, and
represents the wavelength of this wave.
The given in this problem is that two balls are thrown at different times, different heights and velocities. A blue ball is thrown upward at a specific velocity at a lower altitude while a red ball is thrown downwards at a specific speed and at a higher height. In this case, we are asked here to describe the graph of the behavior of the balls as a function of time. The x-axis then is time while the y-axis is the velocity of the ball. The blue ball has a quadratic function while the red ball is more or less exponential. See the attached figure for reference.
