Question

A cheetah can run at a maximum speed

95.9 km/h and a gazelle can run at a maximum
speed of 72.3 km/h.
If both animals are running at full speed,
with the gazelle 68.8 m ahead, how long before
the cheetah catches its prey?
Answer in units of s.

Answer 1

10.6 s

Step-by-step explanation:

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

- Cheetah:
`v_c = 95.9 km/h \cdot (1000 m/km)/(3600 s/h)=26.6 m/s`

- Gazelle:
`v_g =72.3 km/h \cdot (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=(68.8)/(6.5)=10.6 s`