Question
If retardation produced by air resistance of projectile is one-tenth of acceleration due to gravity, the time to reach maximum height
A.
decreases by 11 percent
B.
increases by 11 percent
C.
decreases by 9 percent
D.
increases by 9 percent
Answer :
decreases by 9 percent
Solution :
The time to reach the maximum height without air resistance; $${t_1} = \frac{u}{g} = \frac{u}{{10}},$$
and with air resistance, $${t_2} = \frac{u}{{10 + 1}} = \frac{u}{{11}}$$
$$\eqalign{
& = \frac{{{t_1} - {t_2}}}{{{t_1}}} \times 100 = \left[ {\frac{{\frac{u}{{10}} - \frac{u}{{11}}}}{{\frac{u}{{10}}}}} \right] \times 100 \cr
& = 9\% \left( {{\text{decreases}}} \right) \cr} $$