When two objects move uniformly toward each other, they get 3.0 m closer each second, and when they move uniformly in the same direction with their original speeds, they get 1.0 m closer each 17 seconds. What is the speed (in meters/second) of the faster moving object?
Let V1 be the higher speed and V2 the lower
V1 + V2 = 3.0 m/s
V1 - V2 = 1/17 m/s = 0.0588 m/s
2V1 = 3.0588 m/s
V1 = 1.529 m/s
V2 = 1.471 m/s
To find the speed of the faster moving object, we can set up a system of equations based on the given information.
Let's use the following variables:
- Let v1 be the speed of the faster moving object (in m/s)
- Let v2 be the speed of the slower moving object (in m/s)
Based on the first statement, when the objects move towards each other, they get 3.0 m closer each second. This means that their combined speed is 3.0 m/s. Since they are moving towards each other, we can add their speeds to get:
v1 + v2 = 3.0 -------- Equation 1
Based on the second statement, when they move in the same direction with their original speeds, they get 1.0 m closer each 17 seconds. This means that their relative speed is 1.0 m/17s. Since they are moving in the same direction, we can subtract their speeds to get:
v1 - v2 = 1.0/17 -------- Equation 2
Now, we can solve this system of equations to find the values of v1 and v2.
Adding Equation 1 and Equation 2, we get:
(v1 + v2) + (v1 - v2) = 3.0 + 1.0/17
2v1 = 3.0 + 1.0/17
2v1 = (51 + 1)/17
2v1 = 52/17
v1 = (52/17)/2
v1 = 26/17
Therefore, the speed of the faster moving object is 26/17 m/s, which is approximately 1.529 m/s