Project ForgeM and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?
- A18.60
- B22.50
- 20.61
- D25.00
Explanation
Place the start at (0,0), East=+x, North=+y. M: East 10km -> (10,0); then North-East 10km at 45 degrees -> add (10cos45, 10sin45) = (7.07, 7.07), giving M=(17.07, 7.07). N: South 5km -> (0,-5); then South-East 4km at 45 degrees below East -> add (4cos45, -4sin45) = (2.83, -2.83), giving N=(2.83, -7.83). Distance = sqrt((17.07-2.83)^2 + (7.07-(-7.83))^2) = sqrt(14.24^2 + 14.90^2) = sqrt(202.8+222.0) = sqrt(424.8) = 20.61.
Source: GATE ME 2016 Set-3 (2016)
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