A (2, 4)
B (4, 4)
C (6, 3)
Which of these objects would reach 100 feet in the least amount of time
To determine which object would reach 100 feet in the least amount of time, we need to calculate the speed of each object.
The speed of an object can be calculated using the formula:
speed = distance / time
Let's assume the distance covered by each object is 100 feet. We can find the time taken by each object by rearranging the formula:
time = distance / speed
For object A (2, 4), we need to calculate the speed using the coordinates. We can use the horizontal distance as the speed and calculate the time taken to cover 100 feet:
Time taken by object A = 100 feet / (4 - 2) = 100 feet / 2 = 50 seconds
For object B (4, 4), the horizontal distance is 0 since the x-coordinates are the same. However, the vertical distance is 100 feet:
Time taken by object B = 100 feet / (4 - 4) = undefined (division by zero)
For object C (6, 3), the horizontal distance is 2 and the vertical distance is 100 feet:
Time taken by object C = 100 feet / (3 - 4) = -100 feet (negative value, indicating the object is moving downward)
Therefore, object A would reach 100 feet in the least amount of time, taking 50 seconds.
To determine which object would reach 100 feet in the least amount of time, we need to calculate the speed of each object. The speed can be determined by finding the distance traveled divided by the time taken.
First, we need to find the distance each object travels. Since we are given the coordinates of each object, we can use the distance formula to find the distance between each object and a reference point (like the origin).
The distance formula is: √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between each object and the origin:
Distance of object A from the origin:
√((2 - 0)^2 + (4 - 0)^2) = √(2^2 + 4^2) = √(4 + 16) = √20 ≈ 4.47 feet
Distance of object B from the origin:
√((4 - 0)^2 + (4 - 0)^2) = √(4^2 + 4^2) = √(16 + 16) = √32 ≈ 5.66 feet
Distance of object C from the origin:
√((6 - 0)^2 + (3 - 0)^2) = √(6^2 + 3^2) = √(36 + 9) = √45 ≈ 6.71 feet
Now, to determine which object would reach 100 feet in the least amount of time, we need to calculate their speeds.
The speed formula is: speed = distance / time
Since all objects start at the origin (0,0), their initial position is the same. Therefore, the time taken to reach 100 feet will be proportional to the distance traveled. In other words, the object that has to travel the least distance would reach 100 feet in the least amount of time.
From the distances calculated above, we can see that object A has the shortest distance (4.47 feet). This means that object A would reach 100 feet in the least amount of time compared to objects B and C.