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

Answer:

77.35 m / s

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

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

$tan\phi =\frac{-22.66}{73.96}=-0.306$

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