Question

A lion spots a gazelle exposed on the plain. The gazelle is 35m from the bear, at a compass heading of 230 degrees. 5m from the gazelle, at a heading of 190 degrees, is the gazelle's herd. The top speed of the lion is 10m/s with a maximum acceleration of 5m/s^2 . The speed of the gazelle is 0.9m/s, and it is assumed that it is already moving at this speed. Starting from rest, will the lion be able to catch the gazelle before it reaches it's herd for safety?

*Please answer this to the best of your ability, I'm very confused about it.

Answer 1

We shall take bear and lion as one as necessary info is not given to say that they are differnet and now ( and really! Bears and gazelles are in different habitats. thats common sense)

there are three possibilites

1) Lion chases after the gazelle so the instantaneous velocity of lion is always pointed towards the gazelle like in the diagram below

Which is complex situation to deal with.( Let me know in the comments if this is the method you are searching for)

Possibility 2 :

The lion goes towards the herd and the gazelle also heads towards heard like below

in this case

The distance covered by the gazelle is 5m @ v=0.9 m/s it takes time t = 5.55 sec

the distance covered by the lion is the third side of the traingle whose side length can be found by vector addition as where a = 5 and b= 35 and the angle is 40

i.e distance is 38.96 m @ maximum case of u=0 and a = 5 m/sec² and v_max = 10 m/sec

it takes time t= 4.86 sec

so the lion is able to catch teh gazelle

I hope you found my answer useful, if you did thumbs ups are appreciated

Comment below if you have any doubts or isssues and I will get back

Peace

VK