Question

A point has simultaneous velocities represented by u,2u, 3√3u and 4u. The angle between the first and second and third and fourth are respectively 60° 90° and 150° . The angle the resultant velocity makes with u is -
1) 120°
2) 60°
3)150°
4)30°

Answer 1

Answer:

120°

Explanation:

To make it simplify let say u is at + Ve axis

u  = uCos0° i   + uSin0°j  = u i

Angle between u & 2u is 60°

 2ucos60°i + 2uSin60°j

= u i   + u√3 j

Angle between 2u & 3√3u is 90°

=> Angle between u & 3√3u is 60 + 90 = 150°

 3√3ucos150°i + 3√3uSin150°j

= -u9/2 i  + 3√3u/2 j

Angle between 3√3u & 4u is 150°

=> Angle between u & 4u is 150 + 150° = 300°

4ucos300°i + 4uSin300°j

= 2u i - u2√3j

Resultant =  u i  + u i   + u√3 j  -u9/2 i  + 3√3u/2 j+ 2u i - u2√3j

= -ui/2  + u√3/2 j

Angle = Tan⁻¹((√3/2)/(-1/2)) = Tan⁻¹(- √3) = 120°