An LSU football defender is 6 m behind a Georgia Tech receiver who has the football
and is d meters from making a touchdown. If the LSU player is running at 5 m/s and the
receiver is running at 4 m/s, what is the furthest distance, d, that the Tech player can be
from the goal line and still make a touchdown?
Eq1: 4*t = d
Eq2: 5*t = 6 + d
In Eq2, replace d with 4t:
5t = 6 + 4t
5t-4t = 6
t = 6 s.
In Eq1, replace t with 6:
d = 4 * 6 = 24 m.
To find the furthest distance, d, that the Georgia Tech player can be from the goal line and still make a touchdown, we can use a simple analogy of the players running towards the goal line.
Let's consider the time it takes for the LSU player to catch up to the Georgia Tech player. The LSU player is running at 5 m/s, while the Georgia Tech player is running at 4 m/s.
The relative speed between the two players is the difference in their speeds, which is 5 m/s - 4 m/s = 1 m/s.
The time it takes for the LSU player to catch up to the Georgia Tech player can be found by dividing the initial distance between them (6 m) by the relative speed (1 m/s):
Time = Distance / Speed
Time = 6 m / 1 m/s
Time = 6 seconds
Now, let's find the distance the Georgia Tech player can run during this time.
Distance = Speed x Time
Distance = 4 m/s x 6 s
Distance = 24 m
Therefore, the furthest distance, d, that the Georgia Tech player can be from the goal line and still make a touchdown is 24 meters.
To find the furthest distance, d, that the Georgia Tech receiver can be from the goal line and still make a touchdown, we need to calculate the time it takes for the LSU defender to reach the receiver.
We can start by finding out how long it takes for the LSU defender to close the initial distance of 6 meters between them. We can use the formula:
time = distance / speed.
The distance is 6 meters, and the speed of the LSU defender is 5 m/s. Plugging in these values, we get:
time = 6 m / 5 m/s = 1.2 seconds.
In 1.2 seconds, the LSU defender will have closed the initial 6-meter gap.
Now, we need to determine how far the receiver can travel in this time. We can calculate the distance using the formula:
distance = speed x time.
The speed of the receiver is 4 m/s, and the time is 1.2 seconds. Plugging in these values, we get:
distance = 4 m/s x 1.2 s = 4.8 meters.
Therefore, the furthest distance, d, that the Georgia Tech receiver can be from the goal line and still make a touchdown is 4.8 meters.