Theory question 115
Statics(a) A(−1, 2), B(3, 5) and C(4, 8) are the vertices of triangle ABC. Forces whose magnitudes are 5N and 3√10 N act along AB and CB respectively. Find the direction of the resultant of the forces.
(b) A particle starts from rest and moves in a straight line. It attains a velocity of 20 ms−1 after covering a distance of 8 metres. Calculate: (i) its acceleration; (ii) the time it will take to cover a distance of 40 metres.
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(a) AB = (4, 3), |AB| = 5: force = (4, 3).
CB = (−1, −3), |CB| = √10: force = 3√10 × (−1, −3)/√10 = (−3, −9).
Resultant = (1, −6): 80.5° below the positive x-axis (279.5° anticlockwise from the x-axis; bearing 170.5°).
(b)(i) v² = 2as: 400 = 16a, a = 25 ms⁻².
(ii) 40 = ½(25)t², t² = 3.2, t ≈ 1.79 s.
Force along a line = magnitude × unit vector of that line.