Life Guards

BRITAINS Lead Toy Soldier MOUNTED LIFE GUARD
BRITAINS Lead Toy Soldier MOUNTED LIFE GUARD
$5.00

BRITAIN SOLDIERS LIFE GUARDS IN WINTER CLOAKS WITH OFFICER  5 PCS  SET # 400
BRITAIN SOLDIERS LIFE GUARDS IN WINTER CLOAKS WITH OFFICER 5 PCS SET # 400
$100.00

Vintage Britains Plastic Life Guards
Vintage Britains Plastic Life Guards
$8.00

[63223] W. BRITAIN SET No. 2029 THE LIFE GUARDS (MOUNTED and FOOT SENTRIES)
[63223] W. BRITAIN SET No. 2029 THE LIFE GUARDS (MOUNTED and FOOT SENTRIES)
$49.99

2 Britains Toy Soldiers Lifeguards Life Guards
2 Britains Toy Soldiers Lifeguards Life Guards
$10.00

Cassandra 0050 The Life Guards Mounted 2001
Cassandra 0050 The Life Guards Mounted 2001
$19.00

BRITAINS THE LIFE GUARDS MOUNTED AND FOOT No.2029 w/ORIGINAL BOX  *BEAUTIFUL*
BRITAINS THE LIFE GUARDS MOUNTED AND FOOT No.2029 w/ORIGINAL BOX *BEAUTIFUL*
$119.95

BRITAINS Lead Toy Soldier LIFE GUARD FOOT SENTRY
BRITAINS Lead Toy Soldier LIFE GUARD FOOT SENTRY
$3.99

Britains Swedish Svea Life Guard x 8, including officer, Made in England
Britains Swedish Svea Life Guard x 8, including officer, Made in England
$27.00

Vintage Britains Mounted Life Guards in Winter Cloaks Lot of 3
Vintage Britains Mounted Life Guards in Winter Cloaks Lot of 3
$15.00

WoD054 Life Guards Trooper by King & Country
WoD054 Life Guards Trooper by King & Country
$125.00

Britains Life Guard Toy Soldier
Britains Life Guard Toy Soldier
$10.00

1800's - LIFE GUARDS - 1 (see face)  single vintage playing cards
1800's - LIFE GUARDS - 1 (see face) single vintage playing cards
$0.99

Britains Soldiers Set 2035 Swedish Svea Life Guards Ceremonial Dress Post War
Britains Soldiers Set 2035 Swedish Svea Life Guards Ceremonial Dress Post War
$175.00

Vintage Britains Lead Toy Soldiers Royal Life Guards on Horses lot of 6
Vintage Britains Lead Toy Soldiers Royal Life Guards on Horses lot of 6
$12.50

Britains Lead Toys Mounted Life Guards Set of 10
Britains Lead Toys Mounted Life Guards Set of 10
$19.99

Britains Ltd Boxed Set of (6) 'The Life Guards of The Household Cavalry
Britains Ltd Boxed Set of (6) 'The Life Guards of The Household Cavalry"
$250.00

Wm Britain (1:32) Life Guard #41066 - Special Sale!
Wm Britain (1:32) Life Guard #41066 - Special Sale!
$7.95

Toy Soldier Great Britain 1970 Life Guard 4
Toy Soldier Great Britain 1970 Life Guard 4" Lead figure 1978 IN BOX
$9.99

Crescent Toy Soldier 2202 Grenadier Life Guards And Guards Display Post War
Crescent Toy Soldier 2202 Grenadier Life Guards And Guards Display Post War
$135.00

W.Britians  Vintage The Band Of the 1st Life Guard 1 figure
W.Britians Vintage The Band Of the 1st Life Guard 1 figure
$9.50

Very Early BRITAINS 5 Lead pre-war HORSE Figures LIFE GUARDS
Very Early BRITAINS 5 Lead pre-war HORSE Figures LIFE GUARDS
$49.00

Lot of 6 Keystone Stereoviews ~ WW1 Marching Soldiers, Tanks, 1st Life Guards
Lot of 6 Keystone Stereoviews ~ WW1 Marching Soldiers, Tanks, 1st Life Guards
$12.00

Cherilea Toy Soldiers S202 Life Guards Post War 7 Figures British
Cherilea Toy Soldiers S202 Life Guards Post War 7 Figures British
$75.00

Britains Swoppets  or Eyes Right Mounted Life Guards # 803 Lot of 6
Britains Swoppets or Eyes Right Mounted Life Guards # 803 Lot of 6
$22.99

BRITAINS, LIFE GUARD, CAST METAL
BRITAINS, LIFE GUARD, CAST METAL
$10.00

Britain's The Life Guards, Farrier with Axe Mounted (1pc)
Britain's The Life Guards, Farrier with Axe Mounted (1pc)
$25.00

BRITAIN SOLDIERS LIFE GUARDS MOUNTED AT THE WALK WITH OFFICER  5  PCS.  SET # 1
BRITAIN SOLDIERS LIFE GUARDS MOUNTED AT THE WALK WITH OFFICER 5 PCS. SET # 1
$80.00

Playmobil,LIFE GUARDS,Male & Female,BAY WATCH
Playmobil,LIFE GUARDS,Male & Female,BAY WATCH
$11.99

BRITAINS 41066 LIFE GUARDS FOOT (9PC)
BRITAINS 41066 LIFE GUARDS FOOT (9PC)
$45.00

W Britain 49033 British 1893 1st Life Guards Trooper Archive Collection Soldier
W Britain 49033 British 1893 1st Life Guards Trooper Archive Collection Soldier
$45.00

Ocean City,NJ-BEACH LIFE GUARDS w OARS,RESCUE BOAT,PORT-O-CALL HOTEL,OLD LADY-PC
Ocean City,NJ-BEACH LIFE GUARDS w OARS,RESCUE BOAT,PORT-O-CALL HOTEL,OLD LADY-PC
$4.49

Britain's 7205 Life Guards (Trooper, Standard, Trumpeter) 3pcs
Britain's 7205 Life Guards (Trooper, Standard, Trumpeter) 3pcs
$35.00

1901-07 The Life Guards at Atlantic City, NJ New Jersey PC
1901-07 The Life Guards at Atlantic City, NJ New Jersey PC
$5.95

WoD052 Life Guards Officer by King & Country
WoD052 Life Guards Officer by King & Country
$129.00

ALL ORIGINAL BRITAINS FIRST LIFE GUARD ON HORSE ANTIQUE TOY SOLDIERS (ShS120)
ALL ORIGINAL BRITAINS FIRST LIFE GUARD ON HORSE ANTIQUE TOY SOLDIERS (ShS120)
$19.00

NIB METAL MODELS #7226
NIB METAL MODELS #7226 "2 SCOTS GUARDS, 2 LIFEGUARDS, 2 YEOMAN of the GUARD"
$24.95

Timpo Recast British Life Guards w Cloned Italeri Horses 54mm unpainted plastic
Timpo Recast British Life Guards w Cloned Italeri Horses 54mm unpainted plastic
$12.50

Breyer Horses #3368 Life Guards of Queen's Household Cavalry NIB
Breyer Horses #3368 Life Guards of Queen's Household Cavalry NIB
$65.00

Great Britain WWI 2nd Life Guards Delandre Vignette
Great Britain WWI 2nd Life Guards Delandre Vignette
$5.00

Britains 41066 Life Guards FOOT (8PC)
Britains 41066 Life Guards FOOT (8PC)
$40.00

Napoleonic Wars Cavalry Officer 1st British Life Guards metal figure soldiers N5
Napoleonic Wars Cavalry Officer 1st British Life Guards metal figure soldiers N5
$18.90

Britains Toy Soldiers Set 7247 Lifeguard Trumpeter
Britains Toy Soldiers Set 7247 Lifeguard Trumpeter
$12.99

Britains Toy Soldiers Set 7230 Lifeguard Mounted
Britains Toy Soldiers Set 7230 Lifeguard Mounted
$12.99

HAMLEY'S Britain Ceremonial Special Edition #4021 LIFE GUARD SET NM/MIB
HAMLEY'S Britain Ceremonial Special Edition #4021 LIFE GUARD SET NM/MIB
$69.99

W.Britains Life Guard Mounted 41074
W.Britains Life Guard Mounted 41074
$20.00

Tin Soldiers * Unter officer Life Guards Regiment. Russia  * 54-60 mm *
Tin Soldiers * Unter officer Life Guards Regiment. Russia * 54-60 mm *
$8.00

Frontline Figures: 1FG.7 British 1st Life Guards Standard Bearer with Flag
Frontline Figures: 1FG.7 British 1st Life Guards Standard Bearer with Flag
$68.00

W. BRITAIN Century Collection Life Guard 1837
W. BRITAIN Century Collection Life Guard 1837
$29.99

ATLANTIC CITY, New Jersey NJ    LIFE GUARDS  Marching on Boardwalk 1922 Postcard
ATLANTIC CITY, New Jersey NJ LIFE GUARDS Marching on Boardwalk 1922 Postcard
$6.38

Vintage Britains Set No. 2067 Sovereign's Standard of Life Guards and Escort (7)
Vintage Britains Set No. 2067 Sovereign's Standard of Life Guards and Escort (7)
$69.99

VINTAGE FRAMED SANTA MONICA BEACH PHOTO PIER LIFE GUARDS
VINTAGE FRAMED SANTA MONICA BEACH PHOTO PIER LIFE GUARDS
$24.99

Britain's 7247 Life Guards, Trumpeter
Britain's 7247 Life Guards, Trumpeter
$25.00

6 Denmark Danmark Stereoviews Fredensborg Palace Royal Life Guards and Others
6 Denmark Danmark Stereoviews Fredensborg Palace Royal Life Guards and Others
$12.50

THE ROYAL SALUTE Band Of The Life Guards CD NEW
THE ROYAL SALUTE Band Of The Life Guards CD NEW
$4.95

(3) Britans Queen Elizabeth II on mounted horse
(3) Britans Queen Elizabeth II on mounted horse "Burmese" + horse and life guard
$28.00

Lot of (8) Vintage Britains LTD Painted Lead Toy Soldiers ~ Life Guard ~ Mounted
Lot of (8) Vintage Britains LTD Painted Lead Toy Soldiers ~ Life Guard ~ Mounted
$14.99

Britains Royal Guards, Lifeguard
Britains Royal Guards, Lifeguard
$16.98

King & Country - Napoleonic British Life Guards Charging Bugler NA260 Cavalry
King & Country - Napoleonic British Life Guards Charging Bugler NA260 Cavalry
$99.99

Rare Queensberry Staffordshire England
Rare Queensberry Staffordshire England "Captain of the Life Guards" Coaster Dish
$8.99

DUCAL MODEL THE LIFE GUARDS MOUNTED CORPORAL
DUCAL MODEL THE LIFE GUARDS MOUNTED CORPORAL
$50.00

Britains Toy Soldiers Set 7228 3 Mounted Lifeguards
Britains Toy Soldiers Set 7228 3 Mounted Lifeguards
$29.00

2nd Life Guards, Kings Guard, unused Tuck Oilette
2nd Life Guards, Kings Guard, unused Tuck Oilette
$6.95

King & Country - Napoleonic British Life Guards Guidon Bearer NA261 Cavalry
King & Country - Napoleonic British Life Guards Guidon Bearer NA261 Cavalry
$107.99

2nd Life Guards, State Trumpeter, unused Tuck Oilette
2nd Life Guards, State Trumpeter, unused Tuck Oilette
$6.95

2 VINTAGE BRITISH MILITARY MEDALS THE LIFE GUARDS & ENFIELD 303 RIFLE
2 VINTAGE BRITISH MILITARY MEDALS THE LIFE GUARDS & ENFIELD 303 RIFLE
$14.99

1893 1st Life Guards Trooper, W. Britain 120th Anniversary Piece  #49033
1893 1st Life Guards Trooper, W. Britain 120th Anniversary Piece #49033
$49.99

LIFE GUARDS IN THE HAMPTONS - CELIA JEROME (PAPERBACK) NEW
LIFE GUARDS IN THE HAMPTONS - CELIA JEROME (PAPERBACK) NEW
$10.67

Britains Toy Soldiers Set 9205 Life Guards Mounted in Cloaks
Britains Toy Soldiers Set 9205 Life Guards Mounted in Cloaks
$49.00

Paint & Collect 1:32 Metal Figures Life Guard & Blues & Royals 1999 W Britain
Paint & Collect 1:32 Metal Figures Life Guard & Blues & Royals 1999 W Britain
$9.75

Life Guards to the Rescue Atlantic City  NJ                          6800
Life Guards to the Rescue Atlantic City NJ 6800
$2.30

1955 London Life Guards British Travel Association Print Ad
1955 London Life Guards British Travel Association Print Ad
$14.99

BRITAINS HOUSEHOLD CAVALRY/ LIFE GUARD W/ SWORD METAL FIGURINE NEW #62984
BRITAINS HOUSEHOLD CAVALRY/ LIFE GUARD W/ SWORD METAL FIGURINE NEW #62984
$25.00

William Britain British Life Guard 41066
William Britain British Life Guard 41066
$22.50

PLAYMOBIL 5769 Beach Rescue Life Guard Boat
PLAYMOBIL 5769 Beach Rescue Life Guard Boat
$15.00

St. Petersburg, Mounted Officer, Hussar, Life Guard Regement
St. Petersburg, Mounted Officer, Hussar, Life Guard Regement
$55.00

1915-1920 Venice Beach Life Guards, CA Vintage Photograph 8.5
1915-1920 Venice Beach Life Guards, CA Vintage Photograph 8.5" x 11" Reprint
$7.64

Britains Soldiers 8829 Second Life Guards Special Collectors Edition MIB
Britains Soldiers 8829 Second Life Guards Special Collectors Edition MIB
$79.00

Tuck's 2nd Life Guards  series - Farrier Shoeing  (unused)
Tuck's 2nd Life Guards series - Farrier Shoeing (unused)
$12.99

1973 STANDARD BEARER LIFE GUARDS - UNIFORM ART POSTCARD
1973 STANDARD BEARER LIFE GUARDS - UNIFORM ART POSTCARD
$5.35

Toy Soldier 54mm Greenwood & Ball Life Guard
Toy Soldier 54mm Greenwood & Ball Life Guard
$20.00

ATLANTIC CITY NJ LIFE GUARDS HOSPITAL TENT~DROWNED ARE CARED FOR~ POSTCARD 1910s
ATLANTIC CITY NJ LIFE GUARDS HOSPITAL TENT~DROWNED ARE CARED FOR~ POSTCARD 1910s
$8.32

H.M. Queen Elizabeth's Life Guards - 7 figures - 1:32 Britains' painted metal
H.M. Queen Elizabeth's Life Guards - 7 figures - 1:32 Britains' painted metal
$60.00

Reeves NBC 5 1st LIFE GUARD Household Cavalry Officer 1812-1815 1/32 (54mm)
Reeves NBC 5 1st LIFE GUARD Household Cavalry Officer 1812-1815 1/32 (54mm)
$16.99

DID 1/6 Scale The Life Guards British Royal Dragoons Loose Button Tool
DID 1/6 Scale The Life Guards British Royal Dragoons Loose Button Tool
$4.95

Life Guards Cloth Title British Army
Life Guards Cloth Title British Army
$10.00

1/6 Scale The Life Guards K80108 12 inch Figure DiD USA
1/6 Scale The Life Guards K80108 12 inch Figure DiD USA
$159.99

BUBBAROPE LIFE GUARDS LENGH 2 FEET X 7.500
BUBBAROPE LIFE GUARDS LENGH 2 FEET X 7.500"
$15.00

WoD053 Life Guards Non Commissioned Officer by King & Country
WoD053 Life Guards Non Commissioned Officer by King & Country
$125.00

BRITAINS COLLECTION FOR HARRODS 5878 LIFE GUARD & SCOTS GUARD METAL TOY SOLDIERS
BRITAINS COLLECTION FOR HARRODS 5878 LIFE GUARD & SCOTS GUARD METAL TOY SOLDIERS
$19.95

Chicago Illinois~McKinley Parks~Kids at Swimming Pool~Life Guards~1911 VO Hammon
Chicago Illinois~McKinley Parks~Kids at Swimming Pool~Life Guards~1911 VO Hammon
$4.99

Britains Toy Soldiers Set 8824 Mounted Lifeguard 1837
Britains Toy Soldiers Set 8824 Mounted Lifeguard 1837
$15.99

King & Country - Napoleonic British Life Guard Charging w/ Sword to Rear NA262
King & Country - Napoleonic British Life Guard Charging w/ Sword to Rear NA262
$99.99

1935 Press Photo Life Guards & Royal Horse Guards Passed on Great West Road
1935 Press Photo Life Guards & Royal Horse Guards Passed on Great West Road
$16.88

1939 Tuck's Oilette Postcard - Britain's 1st Life Guards
1939 Tuck's Oilette Postcard - Britain's 1st Life Guards
$5.29

BRITAINS LIFE GUARDS MOUNTED CAVALRY WITH SWORDS LOT OF (4)
BRITAINS LIFE GUARDS MOUNTED CAVALRY WITH SWORDS LOT OF (4)
$40.00

Life Guards in the Hamptons by Celia Jerome Mass Market Paperback Book (English)
Life Guards in the Hamptons by Celia Jerome Mass Market Paperback Book (English)
$11.17

King & Country - Napoleonic British Life Guard Charging w/ Sword Up NA264
King & Country - Napoleonic British Life Guard Charging w/ Sword Up NA264
$99.99

DID  The Life Guards Poster (26 1/2 By 19 1/2).
DID The Life Guards Poster (26 1/2 By 19 1/2).
$20.00

Britains - Two Hand Painted Yeoman of the Guard, Two Hand Painted Lifeguard
Britains - Two Hand Painted Yeoman of the Guard, Two Hand Painted Lifeguard
$15.00

From a raft 50 meters offshore, a life guard wants to swim to shore and run to a snack bar 100 meters down the?

From a raft 50 meters offshore, a life guard wants to swim to shore and run to a snack bar 100 meters down the beach.
a)if the life guard swims at 1 m/s and runs 3 m/s, express the total swimming and running time t as a function the distance x ( in other words, find t(x).
b)using your answer from part , find the minimum time.

Let a 90 degree angle be a point on shore 100 meters from the snack bar and 50 meters from the raft.

Let x = a point on the beach to swim x meters from the right angle
( 0 <= x <= 100 )

Total distance = sqrt(50^2 + x^2) + 100 - x ... in meters

t (x) = sqrt(50^2 + x^2) / 1 + (100 - x) / 3 ... in seconds

t ' (x) = x / sqrt(x^2 + 2500) - 1/3
x / sqrt(x^2 + 2500) - 1/3 = 0
x = 25 / sqrt(2)

t(25/√2) = sqrt(50^2 + (25/sqrt(2))^2) / 1 + (100 - 25/sqrt(2)) / 3
t(25/√2) = 75 / sqrt(2) + (100 - 25/sqrt(2)) / 3

(about) 80.47 seconds
by swimming to a point on the beach
100 - 25/sqrt(2) (about 82.3) meters from the snack bar

Queens Life Guard

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