Question #96184
A cheetah can run at a maximum speed
92 km/h and a gazelle can run at a maximum speed of 72.7 km/h.
If both animals are running at full speed,
with the gazelle 72.9 m ahead, how long before
the cheetah catches its prey?
Answer in units of s. Don't round answer.
1
Expert's answer
2019-10-10T09:53:33-0400

Lets choose coordinate system so that cheetah is at the origin of xx-axis and gazelle LL meters ahead.

The equations of motion of cheetah and gazelle are xC(t)=vCtx_C(t) = v_C t, xG(t)=vGt+Lx_G(t) = v_G t + L respectively, where vC=92kmhv_C = 92 \frac{km}{h} , vG=72.7kmhv_G = 72.7 \frac{km}{h}, L=72.9mL = 72.9 m. When cheetah catches the gazelle, xC(t)=xG(t)x_C(t) = x_G(t), from where vCt=vGt+Lt=LvCvG13.6sv_C t = v_G t + L \Rightarrow t = \frac{L}{v_C - v_G} \approx 13.6 s.


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Comments

Assignment Expert
11.10.19, 17:49

Dear visitor, please use panel for submitting new questions

Maria
11.10.19, 04:12

If both animals are running at full speed, with the gazelle 55.1 m ahead, how long before the cheetah catches its prey? Answer in units of s.

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