Question

Lions can run at speeds up to approximately 80.0 km/h. A hungry 106 kg lion running northward at top speed attacks and holds onto a 37.5 kg Thomson's gazelle running eastward at 77.5 km/h.

Find the final speed ?f of the lion‑gazelle system just after the lion attacks.

Find the angle ?θ between the final velocity of the lion‑gazelle system and the East axis, with positive angles measured counterclockwise from the East axis.

Answer 1

Consider the north-south direction along the y-axis and east-west direction along the x-axis.

In unit vector notation

= initial velocity of lion = 0 i + 80 j

= initial velocity of gazelle= 77.5 i + 0 j

m_L = mass of the lion = 106 kg

m_G = mass of gazelle = 37.5 kg

= final velocity of the lion-gazelle system

Using conservation of momentum

m_L + m_G = (m_L + m_G )

(106) (0 i + 80 j ) + (37.5) (77.5 i + 0 j) = (106 + 37.5)

2906.25 i + 8480 j = 143.5

= 20.25 i + 59.1 j

|| = speed = Sqrt(20.25² + 59.1²) = 62.5 km/h

= angle = tan^-1(59.1/20.25) = 71.1 deg