Some more on projectiles ... A few shortcuts

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19 May 2007 10:11:54 IST

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19 May 2007 10:11:54 IST

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Some more on projectiles ... A few shortcuts

Physics , Mechanics

We all know the standard formulas for range, height and time of flight of a projectile. Consider a problem like this
A particle projected obliquely at 45 deg has a range of 16m. Find the maximum height reached by the particle.
Standard procedure:
Write the formula for Range
Evaluate u.
Find H.
Time taken: 2 min
Lets do summa new.
R = u² sin2/ g
H = u² sin² / 2g
R/H = 4/tan
4H = Rtan
Use this relation
4H = 16 tan45
H = 4
Time taken :5 s
You get the idea. Similarly by doing R/T² , H/T² we get the following set of formulas
4H = Rtan
Rtan =(1/2)gT²
H = (1/8)gT²
Now try solving these problems:
1. The range of a particle thrown at 45 deg is 8m. Find the time of flight.
2. The maximum height reached by a particle thrown obliquely is 2m. Find its time of flight.
Try solving these without using these simplifications once. You'll never let go of these then

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