Intro:
In the savannah, a cheetah is chasing an impala. The impala runs at a constant speed of 16 m/s, with the cheetah initially 10 meters behind and running at 20 m/s but slowing down at 1 m/s². The question is, what will be the gap between them 7 seconds later, and can the impala escape? It’s a high-stakes pursuit, and we’ll use physics to find out.
The scope of this numerical problem encompasses the dynamic pursuit scenario between a cheetah and an impala. It involves applying principles of physics and mathematics to analyze the situation. The problem provides initial conditions, including the impala’s constant speed, the initial distance between the cheetah and the impala, the cheetah’s initial speed, and its rate of deceleration. The primary goal is to formulate a mathematical expression that calculates the gap between the cheetah and the impala as a function of time, denoted as ‘t’ seconds later. Additionally, the problem seeks to answer the crucial question of whether the impala can outrun the cheetah based on the derived expression and its interpretation in the context of the chase.