Question

Determine the magnitude and direction of the resultant velocity of 75.0 m/s. 25.0 east of north, and 100.0 m/s, 25.0 east of south.

Answer 1

77.35 m / s

Ф = -17° from + X axis or 343° from + X axis

Step-by-step explanation:

v1 = 75 m/s 25° east of north

v2 = 100 m/s 25° east of south

Write the velocities in vector form ,we get

`\overrightarrow{v_(1)}=75\left ( Sin25\widehat{i} +Cos25\widehat{j}\right )=31.7\widehat{i}+67.97\widehat{j}`

`\overrightarrow{v_(1)}=100\left ( Sin25\widehat{i} -Cos25\widehat{j}\right )=42.26\widehat{i}-90.63\widehat{j}`

Now add the velocity vectors to get the resultant of the velocities.

`\overrightarrow{v}=\overrightarrow{v_(1)}+\overrightarrow{v_(2)}`

`\overrightarrow{v}=\left (31.7+42.26  \right )\widehat{i}+\left ( 67.97- 90.63 \right )\widehat{j}`

`\overrightarrow{v}=73.96\widehat{i}-22.66\widehat{j}`

magnitude of resultant velocity is
`\sqrt{\left ( 73.96 \right )^(2)+\left ( -22.66 \right )^(2)}`

= 77.35 m / s

The direction is Ф from X axis

`tan\phi =(-22.66)/(73.96)=-0.306`

Ф = -17° from + X axis or 343° from + X axis