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Standard XII

Physics

Angular Velocity

A 2 m wide tr...

Question

A 2m wide truck is moving with a speed of $5 \sqrt{5}$ m/s along a straight horizontal road. A man starts crossing the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v to cross the truck safely is

10 m/s

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5 m/s

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3 m/s

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\frac{5 \sqrt{5}}{2} m / s

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Solution

The correct option is B 5 m/s
$4 + v c o s θ . t = 5 \sqrt{5}$ t (x-axis)
$2 = v s i n θ$ t (y-axis)
$v = \frac{5 \sqrt{5} \times 2}{4 s i n θ + 2 c o s θ}$
Denominator is maximum
$\frac{d D}{d θ} = 0 \Rightarrow t a n θ = 2$
v =5 m/s.

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A 2m wide truck is moving with a speed of 5√5 m/s along a straight horizontal road. A man starts crossing the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v to cross the truck safely is

The correct option is B 5 m/s4+vcos θ.t=5√5 t (x-axis) 2=vsin θ t (y-axis) v=5√5×24sin θ+2 cos θ Denominator is maximum dDd θ=0⇒tan θ=2 v =5 m/s.

A 2m wide truck is moving with a speed of $5 \sqrt{5}$ m/s along a straight horizontal road. A man starts crossing the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v to cross the truck safely is

The correct option is B 5 m/s
$4 + v c o s θ . t = 5 \sqrt{5}$ t (x-axis)
$2 = v s i n θ$ t (y-axis)
$v = \frac{5 \sqrt{5} \times 2}{4 s i n θ + 2 c o s θ}$
Denominator is maximum
$\frac{d D}{d θ} = 0 \Rightarrow t a n θ = 2$
v =5 m/s.