A person is standing on top of a cliff and falls down. If he takes 3.7 s to hit the ground, how high up is the cliff?
1 answer:
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Answer:
Explanation:
Recall the formula for acceleration:
, where
is final velocity,
is initial velocity, and
is elapsed time (change in velocity over this amount of time).
Let's look at our time vs velocity graph. At t=0 seconds, V=25 m/s. So her initial velocity is 25 m/s.
We want to find the acceleration during the first 5 seconds of motion. Well, looking at our graph, at t=5 seconds, isn't our velocity still 25 m/s? Therefore, final velocity is 25 m/s (for this period of 5 seconds).
We are only looking from t=0 seconds to t=5 seconds which is a total period of 5 seconds. Therefore, elapsed time is 5 seconds.
Substituting values in our formula, we have:
Alternative:
Without even worrying about plugging in numbers, let's think about what acceleration actually is! Acceleration is the change in velocity over a certain period of time. If we are not changing our velocity at all, we aren't accelerating! In the graph, we can see that we have a straight line from t=0 seconds to t=5 seconds, the interval we are worried about. This indicates that our velocity is staying the same! At t=0 seconds, we have a velocity of 25 m/s and that velocity stays the same until t=5 seconds. Even though we are moving, we haven't changed velocity, which means our average acceleration is zero!
(a) 0.96 m/s
The period of the wave corresponds to the time taken for one complete oscillation of the boat, from the highest point to the highest point again. Since the time between the highest point and the lowest point is 2.5 s, the period is twice this time:
The frequency of the waves is the reciprocal of the period:
The wavelength instead is just the distance between two consecutive crests, so
And the wave speed is given by:
(b) 0.265 m
The total distance between the highest point of the wave and its lowest point is
d = 0.53 m
The amplitude is just the maximum displacement of the wave from the equilibrium position, so it is equal to half of this distance. So, the amplitude is
(c) Amplitude: 0.15 m, wave speed: same as before
In this case, the amplitude of the wave would be lower. In fact,
d = 0.30 m
So the amplitude would be
Instead, the wave speed would not change, since neither the frequency nor the wavelength of the wave have changed.