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Elanso
2 months ago
6

A Thomson's gazelle can run at very high speeds, but its acceleration is relatively modest. A reasonable model for the sprint of

a gazelle assumes an acceleration of 4.2m/s2
for 6.5 s, after which the gazelle continues continues at a steady speed.
a. What is the gazelle's top speed?
b. A human would win a very short race with a gazelle. The best time for a 30 m sprint for a human runner is 3.6 s. How much time would the gazelle take for a 30 m race?
c. A gazelle would win a longer race. The best time for a 200 m sprint for a human runner is 19.3s.
How much time would the gazelle take for a 200 m race?
Physics
1 answer:
Sav [3.1K]2 months ago
4 0

Answer:

a) 27.3 m/s

b) 3.78 seconds

c) 10.576 seconds

Explanation:

Definitions: t = time elapsed, u = initial speed, v = final speed, s = distance covered, a = acceleration

a)

v=u+at\\\Rightarrow v=0+4.2\times 6.5\\\Rightarrow v=27.3\ m/s

The gazelle's maximum velocity is calculated to be 27.3 m/s.

b)

s=ut+\frac{1}{2}at^2\\\Rightarrow 30=0t+\frac{1}{2}\times 4.2\times t^2\\\Rightarrow t=\sqrt{\frac{30\times 2}{4.2}}\\\Rightarrow t=3.78\ s

It would take the gazelle 3.78 seconds to complete a 30-meter dash.

c)

s=ut+\frac{1}{2}at^2\\\Rightarrow s=0\times 6.5+\frac{1}{2}\times 4.2\times 6.5^2\\\Rightarrow s=88.725\ m

The gazelle accelerates over a distance of 88.725 meters before maintaining constant speed.

Time = Distance divided by Speed

\text{Time}=\frac{200-88.725}{27.3}=4.076\ s

Total time for the gazelle to cover 200 meters equals 6.5 plus 4.076, resulting in 10.576 seconds.

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