Answer:
10.6 s
Explanation:
First of all, let's convert both speeds into m/s:
- Cheetah: [tex]v_c = 95.9 km/h \cdot \frac{1000 m/km}{3600 s/h}=26.6 m/s[/tex]
- Gazelle: [tex]v_g =72.3 km/h \cdot \frac{1000 m/km}{3600 s/h}=20.1 m/s[/tex]
Taking as reference the position x = 0, the position of the cheetah at time t is
[tex]x_c(t) = v_c t[/tex]
while the position of the gazelle, which starts 68.8 m ahead, is
[tex]x_g(t) = 68.8 + v_g t[/tex]
The cheetah catches the gazelle when the two positions are equal:
[tex]x_c = x_g\\v_c t = 68.8 + v_g t[/tex]
and substituting the speeds and solving for t, we find the time at which the cheetah reaches the gazelle:
[tex]26.6t = 68.8 + 20.1 t\\6.5 t = 68.8\\t=\frac{68.8}{6.5}=10.6 s[/tex]
