A lion is watching a zebra from 35m behind it. Both are stationary. The lion then starts chasing by accelerating at a constant rate of 3m/s^2 for 5s. Once at the top speed the lion decelerates at 0.5m/s^2. The zebra starts moving 1s later after the lion started, accelerating at a constant rate of 2m/s^2 for 7s before maintaining a constant speed. a) show that the lion has not caught the zebra after 8s. b) show that the gap between them at time ts, for t>8, after the start of the lion's motion is given by 0.25t^2-5t+51/2, and hence, determine when the lion catches the zebra or when the lion gets closest and how close it gets.
A lion is watching a zebra from 35m behind it. Both are stationary. The lion then starts chasing by accelerating at a constant rate of 3m/s^2 for 5s. Once at the top speed the lion decelerates at 0.5m/s^2. The zebra starts moving 1s later after the lion started, accelerating at a constant rate of 2m/s^2 for 7s before maintaining a constant speed. a) show that the lion has not caught the zebra after 8s. b) show that the gap between them at time ts, for t>8, after the start of the lion's motion is given by 0.25t^2-5t+51/2, and hence, determine when the lion catches the zebra or when the lion gets closest and how close it gets.
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A lion is watching a zebra from 35m behind it. Both are stationary. The lion then starts chasing by accelerating at a constant rate of 3m/s^2 for 5s. Once at the top speed the lion decelerates at 0.5m/s^2. The zebra starts moving 1s later after the lion started, accelerating at a constant rate of 2m/s^2 for 7s before maintaining a constant speed.
a) show that the lion has not caught the zebra after 8s.
b) show that the gap between them at time ts, for t>8, after the start of the lion's motion is given by 0.25t^2-5t+51/2, and hence, determine when the lion catches the zebra or when the lion gets closest and how close it gets.
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