Question

A point which has velocities represented by 7, 8
and 13 is at rest. Find the angle between the
direction of two smaller velocities.
(1) 30°
(2) 45°
(3) 60°
(4) 90°​

Answer 1

answer : option (3) 60°

explanation : from cosine rule of triangle.

$cosA=\left|\frac{b^2+c^2-a^2}{2bc}\right|\\\\cosB=\left|\frac{c^2+a^2-b^2}{2ca}\right|\\\\cosC=\left|\frac{a^2+b^2-c^2}{2ab}\right|$

here a point which has velocities represented by 7, 8 and 13 are at rest.

it means, velocities 7, 8, 13 are sides of a triangle.

Let angle between 7 and 8 (two smaller velocities ) is α.

then, cosα = |(7² + 8² - 13²)/2(7)(8)|

= |(49 + 64 - 169)/112|

= |-56/112|

= |-1/2 | = 1/2 = cos60°

hence, α = 60°

therefore, angle between two smaller velocities (i.e., 7 and 8 ) is 60°.