A car travels 13 km southeast and
then 16 km in a direction 40°
north of east. Find the direction
of
the car's resultant vector.
Answers
Given : A car travels 13 km southeast and then 16 km in a direction 40°
north of east.
To Find : the direction of the car's resultant vector.
Solution:
car travels 13 km southeast
=> 13/√2 km in south and 13/√2 km in East
=> 9.1924 km in south and 9.1924 km in East
=> -9.1924 km in North and 9.1924 km in East
16 km in a direction 40° north of east
=> 16cos40° in East and 16sin40° in North
=> 12.2567 km in East and 10.2846 km in North
Net in East = 9.1924 + 12.2567 = 21.4491 km
Net in North =10.2846 - 9.1924 = 1.0922 km
Net Distance = √(21.4491)² + (1.0922)² = 21.4769 km
angle North of East = tan⁻¹ ( 1.0922/ 21.4491) = 2.915°
21.4769 km in 2.915° north of east
≈ 21.5 km in 2.9° north of east
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Answer:21.5
Step-by-step explanation: