Respuesta :
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
[tex]\overrightarrow{v_{1}}=75\left ( Sin25\widehat{i} +Cos25\widehat{j}\right )=31.7\widehat{i}+67.97\widehat{j}[/tex]
[tex]\overrightarrow{v_{1}}=100\left ( Sin25\widehat{i} -Cos25\widehat{j}\right )=42.26\widehat{i}-90.63\widehat{j}[/tex]
Now add the velocity vectors to get the resultant of the velocities.
[tex]\overrightarrow{v}=\overrightarrow{v_{1}}+\overrightarrow{v_{2}}[/tex]
[tex]\overrightarrow{v}=\left (31.7+42.26 \right )\widehat{i}+\left ( 67.97- 90.63 \right )\widehat{j}[/tex]
[tex]\overrightarrow{v}=73.96\widehat{i}-22.66\widehat{j}[/tex]
magnitude of resultant velocity is [tex]\sqrt{\left ( 73.96 \right )^{2}+\left ( -22.66 \right )^{2}}[/tex]
= 77.35 m / s
The direction is Ф from X axis
[tex]tan\phi =\frac{-22.66}{73.96}=-0.306[/tex]
Ф = -17° from + X axis or 343° from + X axis
