Answer
(a) The falcon changed the raven's direction of motion by an angle of $\theta = 48.0^{\circ}$.
(b) The raven's speed after the collision is 13.5 m/s.
Work Step by Step
(a) We can find the falcon's change in momentum.
$\Delta p = m~\Delta v$
$\Delta p = (0.600~kg)(25.0~m/s)$
$\Delta p = 15.0~kg~m/s$
This change in momentum will be equal to the raven's change in momentum directed at a right angle to its original direction of motion. We can find the raven's initial momentum.
$p = m~v = (1.50~kg)(9.0~m/s)$
$p = 13.5~kg~m/s$
We can find the angle $\theta$ between the raven's original direction and its new direction.
$tan(\theta) = \frac{15.0~kg~m/s}{13.5~kg~m/s}$
$\theta = arctan(\frac{15.0}{13.5})$
$\theta = 48.0^{\circ}$
The falcon changed the raven's direction of motion by an angle of $\theta = 48.0^{\circ}$.
(b) We can find the magnitude of the raven's momentum after the collision.
$p = \sqrt{(15.0~kg~m/s)^2+(13.5~kg~m/s)^2}$
$p = 20.18~kg~m/s$
We can find the raven's speed.
$m~v = p$
$v = \frac{p}{m} = \frac{20.18~kg~m/s}{1.50~kg}$
$v = 13.5~m/s$
The raven's speed after the collision is 13.5 m/s.
