In this problem, let\'s model air resistance by having a projectile in the air l

Question

In this problem, let's model air resistance by having a projectile in the air launched at 45 degrees above +x axis with an x acceleration that is smaller as time goes forward since on average the projectile slows down. Take ax= -aoe-t/t* where t* = total time of trip.
Determine the equation for y(t) for a regular projectile (ax=0) launched with speed of 10m/s at an angle of 45 degrees.
Draw the path in a large graph
Now turn on the air resistance in the model by setting k to be some positive constant such that the maximum x acceleration is 40% gravity; determine the value of ao
Determine v(t) and a(t) in unit vector notation
Write the function r(t) in unit vector notation
Draw the path on the same axes as the first path, and discuss how it is shaped differently from the original path
How do you expect your results to change as ao gets larger and larger?


****Can you just answer the last question please??***** thank you!!

Explanation / Answer

As a0 gets larger, the magnitude of retardation gets larger. The time of flight remains unchanged as no vaiation of acceleration takes place in the y direction. Thus max height reached is the same in all cases too.

However due to the increasing  a0 the Range of the projectile gets smalller & smaller.

Hope only this last part ans helps. This is a question from the 1st chapter of Irodov Physics problems/ May I suggest Abhay Singh's solutions to this book. They are excellent

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