Week 2 - Tutorial 8 sub-question b

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Hello Team,

Ref: Week 2 - Tutorial 8 sub-question b

Slope to Head of T1 = m3 = -1.992

Slope to Foot of T2 = m4 = -1.6

Slope of new torch position SP = m5 = -1.67

As per solution provided:

m3 < m5 implies Head of Thief 1 is not in the range of the torch light

m5 < m4 implies Foot of Thief 2 is in the range of the torch light

Doubt:

m3 < m5 < m4

All this means is that the torch light is falling somewhere between the head of Thief 1 and foot of Thief 2.
With this information how can we conclude that Thief 2 is in the range of the torch light.

Shouldn't we know the NEW angles that the rays are making with the ground (after torch position was changed), to make such conclusions ? 

Regards,

Sandeep 

[Malabika Guha Mustafi]

All this means is that the torch light is falling somewhere between the head of Thief 1 and foot of Thief ( This is only applicable for leftmost ray of torch , which makes a line  at a distance of 48 ft) .

Actually, the torch light (range ) is falling   somewhere between the head of thief 1 and beyond of  Thief 2 head. .

Yes, if we want to get the the range, then we need to know the angle or tan of that ray.

[Mathematics 1 Support 2]

Dear learner,

With the information given to us that m3 < m5 < m4, this means that the torch light doesn't touches the head of T1and also it doesn't touches the leg of T2 either.  And we that M5 is the slope of the initial ray which touches the ground at 48 ft. However the answer lies in the fact that where does the last ray of the torch goes. It should be certainly more than 2ft (Real life explanation:  Sanya is at 80ft above the ground which is nearly to say she is on 4th floor and domestic torch found in home generally covers the ground for a visible range more than 2ft from that height) and therefore T2 who is standing at distance of 50ft falls in visible range of light.

Students are advised to think in real life situation when the questions are real life based. And this question was deliberately given to think like that and not purely based on mathematical explanation. 

Thanks and regards 

Vicky Kumar Sharma 

Maths_1 instructor

IITM Online Degree