Question

The equation of the path of the projectile is $y=0.5x-0.04x^2$ The initials speed of the projectile is

• A. $10m/s$
• B. $15m/s$
• C. $12.5m/s$
• D. None

Answer 1

Answer: (C)

$12.5m/s$

$y=0.5x-0.04x^2=x(0.5-0.04x)$

When $y=0,x=0orR$

$\therefore R=\frac{0.5}{0.04}=12.5$

$y=xtan\theta [1-\frac{x}{R}]\Rightarrow tan\theta =\frac{1}{2};R=12.5m$

But $R=\frac{4u^{2}sin\theta cos\theta }{g}$

$\Rightarrow u=\sqrt{\frac{Rg}{2sin\theta cos\theta }}=\sqrt{\frac{12.5\times 10}{2\times \frac{1}{\sqrt{5}}\times \frac{2}{\sqrt{5}}}}=12.5m/s$