Question

A cheetah can run at a maximum speed

Answer 1

Answer:

10.6 s

Explanation:

First of all, let's convert both speeds into m/s:

- Cheetah: $v_c = 95.9 km/h \cdot \frac{1000 m/km}{3600 s/h}=26.6 m/s$

- Gazelle: $v_g =72.3 km/h \cdot \frac{1000 m/km}{3600 s/h}=20.1 m/s$

Taking as reference the position x = 0, the position of the cheetah at time t is

$x_c(t) = v_c t$

while the position of the gazelle, which starts 68.8 m ahead, is

$x_g(t) = 68.8 + v_g t$

The cheetah catches the gazelle when the two positions are equal:

$x_c = x_g\\v_c t = 68.8 + v_g t$

and substituting the speeds and solving for t, we find the time at which the cheetah reaches the gazelle:

$26.6t = 68.8 + 20.1 t\\6.5 t = 68.8\\t=\frac{68.8}{6.5}=10.6 s$