SATHEE: Kinematics Question 659

Kinematics Question 659

Question: A 2 m wide truck is moving with a uniform speed $v_{0} = 8 m/s$ along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed v when the truck it’s 4 m away from him. The minimum value of v so that he can cross the road safely it’s

Options:

A) 2.62 m/s

B)4.6 m/s

C) 3.57 m/s

D)1.414 m/s

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Let the man starts crossing the road at an angle $θ$ .

For safe crossing the condition it’s that the man must cross the road by the time the truck describes the distance 4 + AC or $4 + 2 c o t θ$ ..

$∴ \frac{4 + 2 \cot θ}{g} = \frac{2 / \sin θ}{v} or v= \frac{8}{2 \sin θ + \cos θ} \dots (i)$

For minimum v, $\frac{dv}{d θ} = 0$

$or \frac{- 8 (2 \cos θ - \sin θ)}{{(2 \sin + c o s θ)}^{2}} = 0$

$or 2 cos θ - \sin θ = 0 or tan θ =2$

$From equation (i),$

$v_{min} = \frac{8}{2 (\frac{2}{\sqrt{5}}) + \frac{1}{\sqrt{5}}} = \frac{8}{\sqrt{5}} = 3.57 m/s$

Kinematics Question 659

Question: A 2 m wide truck is moving with a uniform speed $v_{0} = 8 m/s$ along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed v when the truck it’s 4 m away from him. The minimum value of v so that he can cross the road safely it’s

Options:

Answer:

Solution:

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NCERT Books & Solutions

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Kinematics Question 659

Question: A 2 m wide truck is moving with a uniform speed v0= 8 m/s along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed v when the truck it’s 4 m away from him. The minimum value of v so that he can cross the road safely it’s

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: A 2 m wide truck is moving with a uniform speed $v_{0} = 8 m/s$ along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed v when the truck it’s 4 m away from him. The minimum value of v so that he can cross the road safely it’s