Art and Ben are walking towards a shop along different straight paths.
The diagram shows their position at 3 pm.
a) Assume they walk at the same speed.
Who will arrive at the shop first?
You must show your working.
In your working, let the distance between Ben and the shop be X metres at 3 pm.
Answers
Given : Art and Ben are walking towards a shop along different straight paths.
the distance between Ben and the shop be X metres at 3 pm.
they walk at the same speed.
To Find : Who will arrive at the shop first
Solution:
Distance between art and Shop = 83 m
Distance between Ben and Shop = x m
Distance between art and Ben = 63 m
Angle between Ben Art and Art shop = 74°
Using cosine rule
=> x² = 63² + 83² - 2*63*83Cos74°
=> x² = 3969 + 6889 - 10458*0.2756
=> x² = 3969 + 6889 - 2,882.6
=> x² = 7,975.4
=> x = 89.3 m
83 < 89.3
Hence Art has to cover less distance
Art will take lesser time
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