Question

To practice Problem-Solving Strategy 8.1 Conservation of Momentum. Protecting his nest, a 600-g peregrine falcon rams a marauding 1.5-kg raven in midair. The falcon is moving at 20.0 m/s , and the raven at 9.00 m/s at the moment of impact. The falcon strikes the raven at right angles to the raven's direction of flight and rebounds straight back with a speed of 5.00 m/s . By what angle does the impact change the raven's direction of motion?

Answer 1

The angle as calculated is
`48.013^(\circ)`

Solution:

As per the question:

Mass of falcon,
`m_(f) = 600\ g =0.6\ kg`

Mass of raven,
`m_(r) = 600\ g =0.6\ kg`

Initial speed of the falcon,
`v_(f) = 20.0\ m/s`

Initial speed of the raven,
`v_(r) = 9.00\ m/s`

Rebounding speed of the falcon,
`v'_(f) = - 5\ m/s`

Now,

To calculate the angle at which the direction of motion of the raven changes:

By using the principle of conservation of momentum:

`m_(f)v_(f) + m_(r)v_(r) = m_(f)v'_(f) + m_(r)v'_(r)`

`0.6* 20\hat{j} + 1.5* 9\hat{i} = 0.6* -5\hat{j} + 1.5v'_(r)\hat{i}`

`1.5v'_(r) = 15\hat{j} + 13.5\hat{i}`

`v'_(r) = 9\hat{i} + 10\hat{j}`

The angle of the change of the raven's direction is given by:

`tan\theta = (10)/(9)`

`\theta = tan^(- 1)(1.112) = 48.013^(\circ)`