Question

A cheetah can run at a maximum speed 104 km/h and a gazelle can run at a maximum speed of 74.7 km/h. If both animals are running at full speed, with the gazelle 55 m ahead, how long before the cheetah catches its prey?

Answer 1

It took 6.73 seconds for the cheetah to catch its prey.

Why?

If we want to calculate the time taken for the cheetah to catch its prey, we need to make their equation of position equals.

For the cheetah we have:

`x_(cheetah)=v_(cheetah)*t`

For the gazelle we have:

`x_(gazelle)=55m+v_(gazelle)*t`

Now, substituting and calculating, we have:

`x_(cheetah)=x_(gazelle)`

`v_(cheetah)*t=55m+v_(gazelle)*t`

`104(km)/(h)*t=0.055km+74.7(km)/(h)*t\\\\104(km)/(h)*t-74.7(km)/(h)*t=0.055km\\\\29.3(km)/(h)*t=0.055km\\\\t=(0.055km)/(29.3(km)/(h))=0.00187h=0.00187*3600s=6.73s`

Hence, we have that it took 6.73 seconds to the cheetah to cath its prey.

Have a nice day!