A girl swings on a playgroundswing in such a way that at her highest pointshe is

Question

A girl swings on a playgroundswing in such

a way that at her highest pointshe is 3.1m

from the ground, while at herlowest point she

is 0.5 m from the ground.

What is hermaximum speed? Answer in

Given: In the followingchoices, htop is the

height of the highestpoint and hbot is the

height of the lowestpoint.

At what height above theground will the

girl be moving at a speedhalf of her maximum

speed?

a) h1/2 =(1/2)htop

b) h1/2 =htop

c) h1/2 =(1/4) htop

d) h1/2 = 1/4(3htop + hbot)

e) h1/2 = 1/2(htop + hbot)

f) h1/2 =1/2 (htop)

g) h1/2 = 1/4(htop + hbot)

h) h1/2 =hbot

i) h1/2 =1/2 [htop + (2-1)hbot

j) h1/2 =3/4(htop)

Explanation / Answer

given the maximum height H = 3.1 m the minimum height is h = 0.5 m let the maximum velocity be V , which will be at theminimum height from the conservation of the energy we have                              mgH = mgh + 1/2mV2                                       V = g ( H-h )                                           = ---------- m/s plug in the values and calculate
let at heigth h' , the speed (v ) of the girl is half of hermaximum speed (V ) then according to the conserbvation of the energy we have                       mgh + 1/2mV2 = mgh' + 1/2 mv2                      gh + 1/2V2 = gh' + 1/2(V/2)2                       h ' = (h + V2 /2g)                            = --------- m plug in and calculate                       h ' = (h + V2 /2g)                            = --------- m plug in and calculate

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