Question

Help me out with this problem! :),

Answer 1

Correct Option (3) 3.57 m s-¹

Explanation:

For safe crossing, the condition is that the man must cross the road by the time the truck covers the distance 4 + AC or 4 + 2cot θ.

$\bf \therefore \frac{4 + 2cot \: θ}{8} = \frac{2/sinθ}{v}$

$\bf \: Or, \: \: v = \frac{8}{2 \: sin \: θ + cos \: θ} \: ...(1)$

For Minimum v,

$\bf\frac{dv}{dθ} = 0$

$\bf \implies \: tan \: θ = 2$

From Equation (i),

$\bf \: vmin = \frac{8}{ \sqrt{5}}$

$\bf = 3.57 \: m/s.$