First slide

Projection Under uniform Acceleration

Question

If retardation produced by air resistance of projectile is 1/10 of acceleration due to gravity, the time to reach maximum height

Easy

A

decreases by 11%
B

increases by 11%
C

decreases by 9%
D

increases by 9%

Solution

We know that,
$T = usin θ / g$
If a is retardation caused due to air resistance, then total retardation, a' = (g + a). Now
$T^{'} = \frac{usin θ}{(g + a)}$
Substituting a = (g / 10), we get
$T^{'} = \frac{usin θ}{[g + (g / 10)]} = \frac{10 usin θ}{11 g} = \frac{10}{11} T$
The percentage decrease in time is given by
$\frac{T - T^{'}}{T} \times 100 = \frac{T - (10 T / 11)}{T} \times 100 = 9 %$

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