A hiker walks 20 Km towards the North, then 15 Km Southwards, then 10 Km Eastwards, and finally 12 Km at 30º due East. What is the hiker´s displacement?

Explanation:

We shall represent all displacements in vector form , in terms of i and j . I represents unit displacement towards east and j represents unit displacement in north direction .

First displacement D₁ = 20 j

second displacement D₂ = -15 j

Third displacement D₃ = 10 i

Fourth displacement D₄ = 12 cos30 i + 12 sin30 j  [ 12 cos 30 is displacement towards east and 12 sin30 is displacement towards north ]

Total displacement = 20 j - 15 j + 10 i + 12 cos30 i + 12 sin30 j

= 5 j + 10 i + 10.4 i + 6 j

= 20.4 i + 11 j

Magnitude of displacement = √ ( 20.4² + 11² )

= √ ( 416.16 + 121)

= √ 537.16

= 23.17 m

  1.the balanced   chemical equation is as below

cu +   2 ag(no)₃ → cu(no₃)₂   +2 ag

2.the   much silver   produced   is   50.9 g

step 1: find the   moles of cu

moles =   mass÷   molar mass

  from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236   moles

step 2: use the mole ratio to determine the   moles of ag

from equation above   cu: ag   is 1: 2

therefore the moles of ag   =0.236   moles   x 2/1 =0.472   moles

step 3: find the mass   of ag

mass = moles x molar mass

from periodic table   the molar mass of ag =107.87 g/mol

mass   = 0.472   moles x 107.87 g/mol = 50.9 g

3.   the   much   silver   collected worth is   1.797 oz

  convert   50.9 g   to oz

that is   1 gram = 0.0353 oz

          50.9 grams =?   oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1   gram}   =1.797 oz

answer: a) y=-8x+5

a) m= -8

b) m= -2

c) m= 7

d) m= 6