Jack the Jaguar can run for only 1.0 min at 13.0m/s before he has to stop to rest, while Zeke the zebra can gallop at 7.25m/s for 5.0 min.

1. How long does Zeke actually have to run for to elude Jack?

2. Can Jack catch Zeke for lunch if they are initially 350m apart?

3. Why is this scenario unlikely in the real world?

Please try to give a response to all the questions!!!! It is kinda difficult!

Jack can run 780m in 60 s

Zeke can run 435m in 60s
435+350 = 785
so, what do you think?

To answer these questions, we'll need to apply some basic mathematics and physics concepts.

1. To determine how long Zeke needs to run to elude Jack, we can calculate the distance each animal can cover in their respective times using the formula: distance = speed × time.

For Jack:
distance_Jack = speed_Jack × time_Jack = 13.0m/s × 1.0 min = 13.0m/s × 60s = 780m.

For Zeke:
distance_Zeke = speed_Zeke × time_Zeke = 7.25m/s × 5.0 min = 7.25m/s × 300s = 2175m.

Since Jack can cover a distance of 780m before he needs to rest and Zeke can cover a distance of 2175m, Zeke only needs to run for 780m to elude Jack.

2. To determine if Jack can catch Zeke for lunch, we need to compare the distances they can cover over the same time period. If Jack can catch up to Zeke's initial position within the time it takes Zeke to run away, then Jack can catch him.

Let's denote the initial distance between Jack and Zeke as d_initial, which is 350m in this case.

distance_Jack = speed_Jack × time.
Let's call the time it takes Zeke to run as t_Zeke.

For Jack:
distance_Jack = speed_Jack × time_Jack.

For Zeke:
distance_Zeke = speed_Zeke × t_Zeke.

To solve this, we need to determine when the two distances are equal:
distance_Jack + d_initial = distance_Zeke.

Substituting the values we have:
(speed_Jack × time_Jack) + 350m = (7.25m/s × t_Zeke).

We know that Jack can run for 1.0 min (60 seconds):
So, t_Jack = 60s.

Substituting this value back:
(13.0m/s × 60s) + 350m = (7.25m/s × t_Zeke).

Solving this equation will give the time Zeke runs before Jack catches up to Zeke's initial position. If t_Zeke is greater than or equal to this time, Jack can catch Zeke. Otherwise, Zeke can escape.

3. This scenario is unlikely in the real world due to multiple factors. First, Jaguars usually have a higher top speed than zebras, so it's unusual for a zebra to be able to run away from a jaguar. Additionally, the difference in endurance between these two animals is significantly different. Jack can only maintain his top speed for 1.0 min, while Zeke can gallop for 5.0 min. In reality, jaguars have more stamina and the ability to sustain high speeds for longer periods compared to most zebras. Therefore, it's more likely that the jaguar would catch the zebra unless there were other environmental factors at play, such as obstacles or distance.