got an odd one
a person is being chased by a wombat is running in a straight line towards a tree at a speed of 5.04m/s where the tree is (d) distance away from the person
The wombat is 29.3 m behind the person running at a speed of 9.21m/s
If the person is safe upon reaching the tree whats the maximum value (d) can be for the person to be safe from the wombat
so let's set the d so that the person just reaches the tree at the same time as the wombat. That means that they take the same time (distance/speed) to reach it.
d/5.04 = (d+29.3)/9.21
find d.
person runs distance d
wombat flies distance (d + 23.9)
both go for time t
so
d = 5.04 t so t = d/5.04
(d + 23.9) = 9.21 t
d + 23.9 = 9.21 (d/5.04) = 1.83 d
23.9 = 0.83 d
To find the maximum value of (d) for the person to be safe from the wombat, we need to consider the time it takes for the person to reach the tree and the time it takes for the wombat to catch up to the person.
Let's first find the time it takes for the person to reach the tree. We can use the formula:
Time = Distance / Speed
The distance from the person to the tree is (d). The speed of the person is 5.04 m/s. So, the time it takes for the person to reach the tree is:
Time_person = d / 5.04
Now, let's find the time it takes for the wombat to catch up to the person. The distance between the wombat and the person is 29.3 m. The speed of the wombat is 9.21 m/s. So, the time it takes for the wombat to reach the person is:
Time_wombat = 29.3 / 9.21
For the person to be safe, we need the time it takes for the person to reach the tree to be greater than the time it takes for the wombat to catch up to the person.
Therefore, we have the inequality:
d / 5.04 > 29.3 / 9.21
To find the maximum value of (d), we can solve this inequality for (d). Multiply both sides of the inequality by 5.04 to get:
d > (29.3 / 9.21) * 5.04
Now, we can calculate the maximum value of (d):
d > 16.1434
So, the maximum value of (d) for the person to be safe from the wombat is approximately 16.1434 meters.