Answer
$|V_{PB}| = 24.8m/s$
Work Step by Step
Velocity of B relative to A = $V_{BA}$
Velocity of P relative to A = $V_{PA}$
Velocity of P relative to B = $V_{PB}$
$V_{BA} = (20cos (30^{\circ}) i + 20sin(30^{\circ})j)m/s$
$V_{BA} = (17.3 i + 10j)m/s$
$V_{PA} = (30cos (60^{\circ}) i + 40sin(60^{\circ})j)m/s$
$V_{PA} = (20 i + 34.6j)m/s$
$V_{PB} = V_{PA} -V_{BA}$
$V_{PB} = (20 i + 34.6j)m/s - (17.3 i + 10j)m/s$
$V_{PB} = (20 i - 17.3 i+ 34.6j + 10j)m/s$
$V_{PB} = (2.7i + 24.6j)m/s$
$|V_{PB}| = \sqrt {2.7^2 + 24.6^2}$
$|V_{PB}| = 24.8m/s$
