Question

A projectile is fired at an angle θ with respect to ground. The projectile launch velocity is V m/s. Find the difference between projectile range when there is no air resistance and when air resistance is present. For the case when the air resistance is present assume that the projectile decelerates horizontally at A (m/s2). Express the difference in range between the two situations in terms of θ, A, V and g (where g is the downward acceleration due to gravity). 

          A projectile is fired at an angle θ with respect to ground. The
projectile launch velocity is V m/s. Find the difference between
projectile range when there is no air resistance and when air
resistance is present. For the case when the air resistance is
present assume that the projectile decelerates horizontally at A
(m/s2). Express the difference in range between the two situations
in terms of θ, A, V and g (where g is the downward acceleration due
to gravity).
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A projectile is fired at an angle θ with respect to ground. The projectile launch velocity is V m/s. Find the difference between projectile range when there is no air resistance and when air resistance is present. For the case when the air resistance is present assume that the projectile decelerates horizontally at A (m/s2). Express the difference in range between the two situations in terms of θ, A, V and g (where g is the downward acceleration due to gravity).
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Transcript

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00:01 Hello, we have the source of the following problem.
00:02 Project tile was fired at an angle theta with a velocity v.
00:12 And here we have to calculate the percentage, difference in range when there is no air resistance and with air resistance.
00:24 So let's make the sketch.
00:29 So here we have to calculate delta l in percentage.
00:33 So first, let's look at the motion without any resistance.
00:39 In this case l equals to v0 cosine theta times time of light which is v0 cosine theta times v0 sine theta times 2 and over g.
00:57 Let's call it l1 and that is v0 squared over g sine theta.
01:06 So now, what let's add air resistance.
01:15 This resistance has acceleration a directed to the left.
01:24 It means that now x coordinate as a function of time is v0 cosine teta times time minus et squared over 2.
01:40 And now we have to calculate time of the flight.
01:42 Time of light is the same, that is 2...
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