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 90 percent
• D. increases by 90 percent

Answer 1

The Correct Option is C

Suppose $t_{0}$ be the time to reach maximum height in the absence of air resistance, then from the relation $t_{0}=\frac{u \sin \alpha}{g}$ ...(1) when $a$ is retardation caused by air resistance, then total retardation will be $g+a$ $t_{1}=\frac{u \sin \alpha}{g +a}=\frac{u \sin \alpha}{g+\left(\frac{1}{10}\right) g}$ $=\frac{10 u \sin \alpha}{11 g}$ ...(2) Now from equations (1) and (2), we have $t_{1}=\frac{10}{11} t_{0}$ or $t_{1}=90 \% t_{0}$ Time will decrease by $90 \%$.