Answer :
Final answer:
The lion and gazelle's combined momentum is calculated considering the direction of their movement (north and east respectively). The total momentum after the attack will equal the total momentum before the attack, as per the conservation of momentum principle. Thus, their speed post-attack is approximately 68.03 km/hr.
Explanation:
The subject of this question is physics and it pertains to the theory of conservation of momentum. Here, a hungry lion running in the northward direction attacks a gazelle running eastwards. Post the attack, we need to compute their combined speed. We know, in an isolated system, the total momentum before the event is equal to the total momentum after. Hence, we can set up the following mathematical model:
When running northward at 79.1 km/hr, the lion's momentum= 181 kg x 79.1 km/hr = 14320.1 kg km/hr.
The gazelle’s momentum running eastward at 61.4 km/hr = 31.7 kg x 61.4 km/hr = 1946.38 kg km/hr.
As per the theory of vectors, the final resultant momentum (and speed) can be calculated as the square root of the sum of squares of the individual momenta (speeds), which in this case gives √((14320.1)^2 + (1946.38)^2) kg km/hr = 14473.46 kg km/hr.
Thus, the combined mass of the lion and gazelle post-attack = 181kg + 31.7kg = 212.7kg and the speed post-attack = total momentum / total mass = 14473.46 kg km/hr / 212.7 kg = 68.03 km/hr (rounded).
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