Question

distance and displacement

1. find the distance, displacement and direction of displacement for the paths in the following grids.

each square is 1 cm wide.
distance = ______ displacement = ____ direction = ______
distance = ______ displacement = ____ direction = ______

Explanation:

Step1: Calculate distance for first grid

Count number of squares.
$4 + 3=7$ cm

Step2: Calculate displacement for first grid

Use Pythagorean theorem.
$d=\sqrt{1^{2}+2^{2}}=\sqrt{5}$ cm

Step3: Determine direction for first grid

Observe path direction.
South - East

Step4: Calculate distance for second grid

Count number of squares.
$3 + 4=7$ cm

Step5: Calculate displacement for second grid

Use Pythagorean theorem.
$d=\sqrt{2^{2}+3^{2}}=\sqrt{13}$ cm

Step6: Determine direction for second grid

Observe path direction.
South - East

Answer:

For the first grid:

• Distance: 7 cm
• Displacement: $\sqrt{5}$ cm
• Direction: South - East

For the second grid:

• Distance: 7 cm
• Displacement: $\sqrt{13}$ cm
• Direction: South - East