Lions can run at speeds up to approximately 80.0 km/h. A hungry 175-kg lion runn

Question

Lions can run at speeds up to approximately 80.0 km/h. A hungry 175-kg lion running northward at top speed attacks and holds onto a 28.0-kg Thomson's gazelle running eastward at 60.0 km/h. Find the speed of the lion-gazelle system just after the lion attacks. (Express your answer to three significant figures.) Computed value: 60.5 Submitted: Saturday, March 26 at 12:42 PM Feedback: Find the direction of travel of the lion-gazelle system just after the lion attacks. (Express your answer to three significant figures.) north of east Submit

Explanation / Answer

80 km/hr = (5/18) × 80 m/s = 22.22 m/s
60 km/hr = (5/18) × 60 m/s = 16.66 m/s

Momentum of the lion = 175 × 22.22 kg m/s
= 3888.5 kg m/s = p (suppose)

Momentum of the gazelle = 28 × 16.66 kg m/s
= 466.48 kg m/s = q (suppose)

Angle between p and q
= angle between north and east
= 90°

Resultant momentum = r (suppose)

r^2 = p^2 + q^2 + 2pq cos (90°)
= p^2 + q^2

r = sqrt (p^2 + q^2) = 3916.38 kg m/s

Resultant mass = (175+28) kg = 203 kg

Resultant velocity = (resultant momentum) / (resultant mass)
= (3916.38 / 203) m/s
= 19.292 m/s towards north-east

2

angle = arctan (80*175/(60*28)) = 83.15° NoE

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