Need help with this short physics question
there is a race betwen person A and person B. They both start at the same time, but B initial position is 10m left of peron A. person A travels 100 meters right in 20 seonds, Person Btravels 112.5 meters right in 15 seconds.
what is the time, postion and, and person B displacement at which Person B catches up with Person A
Consider person A's starting position to be 0.
for person A, d = r * t
d = 100 meters / 20 sec * t
d = 5 meters / sec * t
for person B, d = 10 + (d * t)
d = 10 + (112.5 meters / 15 sec * t)
d = 10 + (7.5 meters / sec * t)
We know the two positions are equal when person A catches person B. So.
5 meters / sec * t = 10 + (7.5 meters / sec * t)
solving that will give you t.
To find the distance, use the simpler of the 2 original equations:
d = 5 meters / sec * t
i don't get how to find the time
To find the time, position, and person B's displacement at which Person B catches up with Person A, you can use the equation of motion relating position, velocity, and time.
Let's start by setting up a coordinate system where the initial position of Person A is taken as the origin (0 m). Since Person B is initially 10 m left of Person A, we can set Person B's initial position as -10 m.
Now, let's calculate the velocities of both Person A and Person B. The velocity of an object is calculated by dividing the displacement by the time taken. Person A's velocity is 100 m / 20 s = 5 m/s, and Person B's velocity is 112.5 m / 15 s = 7.5 m/s.
To determine when Person B catches up with Person A, we need to find the time at which their positions are the same. This means that the position of Person A at the given time (t) would be equal to the position of Person B at the same time.
Using the equation of motion: position = initial position + velocity * time,
the position of Person A at time (t) is given by A_position = 0 + 5t, and the position of Person B at the same time is B_position = -10 + 7.5t.
To find when B catches up with A, we set A_position equal to B_position:
0 + 5t = -10 + 7.5t.
Now, solve this equation for t:
5t - 7.5t = -10,
-2.5t = -10,
t = 4 seconds.
Therefore, Person B catches up with Person A after 4 seconds.
To find the position at which Person B catches up with Person A, substitute the value of t (= 4 seconds) into either A_position or B_position. Using B_position, we have:
B_position = -10 + 7.5 * 4 = -10 + 30 = 20 meters.
Therefore, Person B catches up with Person A at a position of 20 meters.
Finally, to find Person B's displacement at this moment, we can subtract their initial position from their position at the catching-up point:
Displacement = B_position - B_initial_position,
Displacement = 20 - (-10) = 30 meters.
Thus, Person B's displacement at the moment of catching up with Person A is 30 meters.