a point has simultaneous velocities represented by
u, 2u, 313, and 4u. The angle between the first
and second, the second and third and the third
and fourth are respectively 60°, 90° and 150°. The
angle the resultant velocity makes with us
(1) 120
(2) 60°
(3) 150
(4) 30°
Answers
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°
Answer:
120°
Explanation:
to make it simplify let u is at t veaxis u=u coso°
angle between u &2us in 60°
2ucos 60°j
= hi + u√3j
angle between 2u & 3√3u is 90°
=>angle between u& 3√3u is 60+ sin150°
3√3suco150° i+3√3u sin 150°
angle between 3√ 3u& 4u is150 + 150= 300°
4ucos300i+ 4usin 300°j
= 2ui- 42 √ 3j resultant= ui+ ui+ u√- u 9/ 2i+ 3√3u/u 9/2i+3√3u/2j + 2uiu2
=ui/2+u√3/2j
therefore:
angle= tan-1 [(√3/2)/(-1/3)= tan-1(-√3)=120°