When two objects A and B move with uniform speeds toward each other along a
straight line, they get 5m closer to each other every second. If they move in the
same direction along a straight line with the original speeds they get 1m closer, to
each other every second. The speeds of A and B are respectively
1) 5ms1 and 4ms-1
2) 5 ms-1 and 10ms-1 3) 3ms-1 and 2ms-1?
4) 3ms-1 and Ims-1
5) 2ms-1 and 1ms-1?
the sum is five and the difference is one ... 3 and 2 look good
THANK U
To solve this problem, we can use the concept of relative speed.
When two objects move towards each other, their relative speed is the sum of their individual speeds. Conversely, when two objects move in the same direction, their relative speed is the difference of their individual speeds.
Let's denote the speed of A as "v_A" and the speed of B as "v_B".
According to the given information, when moving towards each other, the objects get 5m closer every second. This means that the relative speed is 5m/s.
Therefore, v_A + v_B = 5 --------(Equation 1)
When moving in the same direction, the objects get 1m closer every second. This means that the relative speed is 1m/s.
Therefore, v_A - v_B = 1 --------(Equation 2)
We now have a system of two equations with two unknowns, v_A and v_B. We can solve this system of equations to find the speeds of objects A and B using any method of algebraic manipulation, such as substitution or elimination.
Let's solve the equations using the method of substitution:
From Equation 1, we can express v_A in terms of v_B as v_A = 5 - v_B.
Substituting this into Equation 2, we get (5 - v_B) - v_B = 1.
Simplifying the equation, we have 5 - 2v_B = 1.
Rearranging, we find -2v_B = 1 - 5.
Simplifying further, we get -2v_B = -4.
Dividing both sides of the equation by -2, we find v_B = 2.
Substituting this value into Equation 1, we get v_A + 2 = 5.
Simplifying, we find v_A = 3.
Therefore, the speeds of objects A and B are 3 m/s and 2 m/s respectively.
So the answer is option 4) 3ms-1 and 2ms-1.