Out on the African savannah, a cheetah is trying to catch a gazelle. This partic

Question

Out on the African savannah, a cheetah is trying to catch a gazelle. This particular cheetah can accelerate from rest to 30.0 m/s in 3.00 s, and then maintain that speed for a maximum of 30.0 s. This particular gazelle can accelerate from rest to 24.0 m/s in 20.0 s, and then maintain that top speed for quite a while.

For parts (a) – (c), let’s say that the cheetah wants to catch the gazelle by the end of the cheetah’s acceleration period. Assume that both animals start from rest at the same time and that the gazelle runs directly away from the cheetah.

(a) How far does the cheetah travel by the end of its acceleration period?

(b) How far does the gazelle travel during that time?

(c) What is the maximum distance the cheetah can be from the gazelle when they both start accelerating so the cheetah catches the gazelle by the end of the cheetah’s acceleration period?

(d) 23.0 s after starting from rest, how far has the cheetah traveled?

Explanation / Answer

a) v=at

a = 10m/sec^2

s =0.5*10*3^2 = 45m

b) v=at

a = 1.2m/sec^2

s =0.5*1.2*3^2 = 4.8m

c) 45-4.8 = 40.2m

d) for first 3 sec 45m

then for next 20 sec

s = v*t = 20*30 = 600m

645m

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