Answer :
Answer:
The angle as calculated is [tex]48.013^{\circ}[/tex]
Solution:
As per the question:
Mass of falcon, [tex]m_{f} = 600\ g =0.6\ kg[/tex]
Mass of raven, [tex]m_{r} = 600\ g =0.6\ kg[/tex]
Initial speed of the falcon, [tex]v_{f} = 20.0\ m/s[/tex]
Initial speed of the raven, [tex]v_{r} = 9.00\ m/s[/tex]
Rebounding speed of the falcon, [tex]v'_{f} = - 5\ m/s[/tex]
Now,
To calculate the angle at which the direction of motion of the raven changes:
By using the principle of conservation of momentum:
[tex]m_{f}v_{f} + m_{r}v_{r} = m_{f}v'_{f} + m_{r}v'_{r}[/tex]
[tex]0.6\times 20\hat{j} + 1.5\times 9\hat{i} = 0.6\times -5\hat{j} + 1.5v'_{r}\hat{i}[/tex]
[tex]1.5v'_{r} = 15\hat{j} + 13.5\hat{i}[/tex]
[tex]v'_{r} = 9\hat{i} + 10\hat{j}[/tex]
The angle of the change of the raven's direction is given by:
[tex]tan\theta = \frac{10}{9}[/tex]
[tex]\theta = tan^{- 1}(1.112) = 48.013^{\circ}[/tex]