23. If a jogger runs 100 meters west and then turns around and runs 30 meters east. What
2 answers:
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Answer:
a)
b) See the proof below
c)
Explanation:
Part a
For this case we have the following differential equation:
With the initial condition
We can rewrite the differential equation like this:
And if we integrate both sides we got:
Where is a constant. If we apply exponential for both sides we got:
Using the initial condition we got:
So then our solution for the differential equation is given by:
For the half life we know that we need to find the value of t for where we have if we use this condition we have:
Applying natural log we have this:
And then the value of t would be:
And using the fact that we have this:
Part b
For this case we need to show that the solution on part a can be written as:
For this case we have the following model:
If we replace the value of k obtained from part a we got:
And we can rewrite this expression like this:
And we can cancel the exponential with the natural log and we have this:
Part c
For this case we want to find the value of t when we have remaining
So we can use the following equation:
Simplifying we got:
We can apply natural log on both sides and we got:
And if we solve for t we got:
We can rewrite this expression like this:
Using properties of natural logs we got:
Answer:
On moon time period will become 2.45 times of the time period on earth
Explanation:
Time period of simple pendulum is equal to ....eqn 1 here l is length of the pendulum and g is acceleration due to gravity on earth
As when we go to moon, acceleration due to gravity on moon is times os acceleration due to gravity on earth
So time period of pendulum on moon is equal to
--------eqn 2
Dividing eqn 2 by eqn 1
So on moon time period will become 2.45 times of the time period on earth