The magnitude of pairs of displacement vectors are given

Asked by admin @ 20/08/2021 in Physics viewed by 287 People

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? (a) 4 cm, 16 cm (b) 20 cm, 7 cm (c) 1 cm, 15 cm (d) 6 cm, 8 cm

Answered by admin @ 20/08/2021

3 answers · Physics

Best Answer

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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