Question

A cheetah can run at a maximum speed 103 km/h and a gazelle can run at a maximum speed of 76.5 km/h. If both animals are running at full speed, with the gazelle 99.3 m ahead, how long before the cheetah catches its prey?
Answer in units of s.


Part 2: The cheetah can maintain its maximum speed for only 7.5 s. What is the minimum distance the gazelle must be ahead of the cheetah to have a chance of escape? (After 7.5 s the speed of cheetah is less than that of the gazelle.)

Answer in units of m.

Answer 1

Answer:

1

 $t_a = 13.49 \ s$

2

 The distance is   $D = 55.2 \ m$    

Explanation:

From the question we are told that

   The maximum speed of the cheetah is  $v = 103 \ km/h = 28.61 \ m/s$

    The maximum of  gazelle is  $u = 76.5 \ km/h = 21.25 \ m/s$

     The distance ahead is $d = 99.3 \ m$

Let  $t_a$ denote the time which the cheetah catches the gazelle

Gnerally the equation representing the distance the cheetah needs to move in order to catch the gazelle is

           $v* t_a = d + u* t_a$

=>          $28.61 t_a = 99.3 + 21.25t_a$

=>          $7.36 t_a = 99.3$

=>         $t_a = 13.49 \ s$

Now at t =  7.5 s  

             $7.5 v = D+ 7.5u$

=>          $28.61 * 7.5 = D + 21.25* 7.5$

=>          $7.36 * 7.5 =D$

=>         $D = 55.2 \ m$        

Hence the for the gazelle to escape the cheetah it must be 55.2 m