Question

physics help

Answer 1

whats up?

Answer 2

its a question on 1 d motion

Answer 3

put the question out.......

Answer 4

wel a man walks with a uniform velocity v towards a lantern of height H from ground

Answer 5

his height is h

Answer 6

find the velocity of the tip of his shadow

Answer 7

when i checked the answer key it is given V*(H-h/h) but i dont knw jow it is got

Answer 8

Nice question. Let the man be distance D from the lamp and the length of his shadow L. Then
H/(D+L) = h/d
=> DH = h(d+L)
=> L = (H-h)/h . D

Now the only thing changing on the RHS is D. We know D is change at a rate of v so rate of change of L is

(H-h)/h . v

Answer 9

(formally, differentiate wrt time L = (H-h)/h . D )

Answer 10

helppppppppppp

Answer 11

What step don't you follow? Draw a diagram certainly to help.

Answer 12

wait dont go away let me read

Answer 13

and draw

Answer 14

post a comment when you're ready and I'll come back.

Answer 15

i am confused which is L and in fig

Answer 16

can u show

Answer 17

..........

Answer 18

.................u thr?

Answer 19

hw=ey there is no small d in fig

Answer 20

d = D. I'm using D

Answer 21

H/(D+L) = h/D
=> DH = h(D+L)
=> L = (H-h)/h . D

Answer 22

L = (H-h)/h . D
(H-h)/h . i didnt get this

Answer 23

??

Answer 24

DH = h(D+L)
=> DH = Dh + Lh
=> Lh = DH - Dh
=> Lh = D(H-h)
=> L = (H-h)/h . D

Answer 25

(H-h)/h . v that step

Answer 26

Now differentiate both sides

dL/dt = (H-h)/h . dD/dt = (H-h)/h . v

Answer 27

wel how we know that this is vlocity of the shadow??

Answer 28

at tip???????/

Answer 29

because L is the length of the shadow so its derivative is its velocity.

Answer 30

but only with respect to the man.

Answer 31

d is length of shadow ryt?

Answer 32

Yes, by defintion and look at the diagram.

with respect to the lamp, the velocity of the the tip of the shadow is
dL/dt + v = (H-h)/h v + v
= H/h . v

Answer 33

pls show the steps of that v w r to lamp

Answer 34

some more

Answer 35

because the man walking towards the lamp at velocity v

Answer 36

Suppose you're walking a dog. You are walking at speed v. And he walking towards you RELATIVE TO YOU at a speed w. Then the dog is walking at speed of v + w

Answer 37

if w = 0 then he is walking at a speed v and hence he doesn't get any closer or farther away

Answer 38

confused :(

Answer 39

Imagine walking a dog. You're walking at speed v. At what speed does he have to walk so he is not closer or farther away from you?

Answer 40

v

Answer 41

yes and what is his velocity relative to you?

Answer 42

0

Answer 43

Now imagine he is walking with velocity of w relative to you. What is his absolute velocity if you are walking with a velocity of v?

Answer 44

w+v

Answer 45

Right. So that is what is going here with the tip of the shadow. The shadow length D was defined relative to the position of the man.

Answer 46

and we found dD/dt, the velocity of the tip of the shadow relative to the man.

Answer 47

The other way to think about this is the position of the tip of the shadow.

That position is L + D

Answer 48

k

Answer 49

hence the velocity of the tip of the shadow is
\[\frac{d \ }{dt} (L + D) = \frac{dL}{dt} + \frac{dD}{dt} = v + \frac{H-h}{h} v = \frac{H}{h}v\]

Answer 50

oh k bt in othr case y we dont find relative velocity ??

Answer 51

dD/dt is the velocity relative to the man.

Answer 52

oh i got it as lamp was at rest we dont consider relative velocity ryt??

Answer 53

I think we can assume the lamp hasn't got legs, yes

Answer 54

again dD/dt is absolute velocity??if it was v with respect to man it shuld be vi H-h/h *v

Answer 55

v-(H-h)/h*v

Answer 56

"a man walks with a uniform velocity v towards a lantern of height H from ground"

Answer 57

Are the man and the tip of the shadow moving in opposite directions? No. So it's addition, not subtraction.

Answer 58

y?????

Answer 59

va- vb when same direction

Answer 60

Why are the man and the tip of the shadow moving in the same direction?

Answer 61

NO. Go back back to our dog example.

Answer 62

in dog example absolute value of dog velocity was w+v

Answer 63

but rel is va-vb

Answer 64

yes. added. that's what we're doing here.

Answer 65

but rel is va-vb we are finding relative here

Answer 66

so it's dD/dt

Answer 67

which is the relative veloiccity of the shadow tip

Answer 68

vs-vman

Answer 69

relative to the man that is, because D itself is measured relative to the man.

Answer 70

oh k

Answer 71

i hav another o ne question

Answer 72

post it separately

Answer 73

:)

Answer 74

physicsss