A man drove his car northward,then turned left and drove 10km and again turned left and drove 20km.He found himself 10km west of his starting point.How far did he drive northward initially?
20km
20
The driver formed a rectangle with 10 km
horizontal sides and 20 km vertical sides(northward).
AB+BC+CD = AD
AB + (-10) + (-20i) = -10
AB = 20i = 20km Northward.
To solve this problem, we can break it down into steps and visualize the movements of the man's car. Let's go through the steps:
1. The man drove his car northward, so initially, he started at point A and moved in a northward direction.
A
↑
2. Then, the man turned left. Since the man turned left after driving north, he would be facing west and continue moving in that direction.
A
←───────── B
↑
3. The man drove 10 km in the westward direction. After driving 10 km westward, he would be 10 km west of point B.
A
←───────── B
C ↑
4. Now, the man turned left again. Since the man turned left after driving west, he would be facing south and continue moving in that direction.
At this point, the man actually made a complete U-turn.
A
←───────── B
│ C ↓
│
D
5. Finally, the man drove 20 km southward. After driving 20 km southward from point C, he ended up at point D, which is 10 km west of the starting point A.
A
←───────── B
│ C │
↓ │ │
D ↓
To find the distance the man initially drove northward, we need to calculate the straight line distance between points A and D.
Using the Pythagorean theorem, we can find this distance:
distance = √(10^2 + 20^2)
distance = √(100 + 400)
distance = √500
distance ≈ 22.36 km
Therefore, the man initially drove approximately 22.36 km northward.