Question

The magnitude of pairs of displacement vectors are given. Which pairs of displacement vectors cannot be added
to give a resultant vector of magnitude 13 cm?
(1) 4 cm, 16 cm (2) 20 cm, 7 cm (3) 1 cm, 15 cm (4) 6 cm, 8 cm

Answer 1

Explanation:

Easy ones first. 

(2) 1cm + 3cm head to tail = 4cm OK 

(3) 5cm - 1cm head to tail = 4 cm OK 

(1) 2cm + 3cm at an angle to each other will make 4cm 

a²+b² = c²+2abcos∅ 

(2cm)² + (3cm)² = (4cm)²+2×(2cm×3cm)cos∅ 

(4+9-16)÷12 = -.25 = cos∅ 

∅ = arc cosine (-.25) 

At this angle 2cm+3cm = 4cm 

(4) 1cm and 7cm can't add or subtract to less than 6cm 

Place 1 and 7 head to tail and rotate either. 

The result can't be less than 6 or more than 8.

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