Respuesta :
Answer:
127.36 m/s
Explanation:
velocity of plane with respect to air = 140 m/s due east
velocity of air with respect to ground = 31 m/s 30° west of north
Write the velocities in the vector forms
[tex]\overrightarrow{V_{p/a}}=140\widehat{i}[/tex]
[tex]\overrightarrow{V_{a/g}}=31 \left ( -Sin30 \widehat{i}+Cos30\widehat{j} \right )[/tex]
[tex]\overrightarrow{V_{a/g}}= -15.5 \widehat{i}+26.85\widehat{j}[/tex]
Let velocity of plane with respect to ground is given by vp/g
According to the formula of relative velocities
[tex]\overrightarrow{V_{p/a}}=\overrightarrow{V_{p/g}}-\overrightarrow{V_{a/g}}[/tex]
[tex]\overrightarrow{V_{p/g}}=\overrightarrow{V_{p/a}}+\overrightarrow{V_{a/g}}[/tex]
[tex]\overrightarrow{V_{p/g}}= \left ( 140-15.5 \right )\widehat{i}+26.85\widehat{j}[/tex]
[tex]\overrightarrow{V_{p/g}}= \left ( 124.5 \right )\widehat{i}+26.85\widehat{j}[/tex]
The magnitude of the velocity of plane with respect to the ground is given by
[tex]V_{p/g} = \sqrt{124.5^{2}+26.85^{2}}=127.36 m/s[/tex]
Thus, the velocity of plane with respect to the ground is given by 127.36 m/s.
