Solving Mechanics Questions: Cyclists A & B, Fly

[Raed]

Homework Statement

Two cyclists, A and B, have displacements 0 Km and 70 Km, respectively. At t = 0 they begin to cycle towards each other with velocities 15 Km/hr and 20 Km/hr, respectively. At the same time, a fly that was sitting on A starts flying towards B with a velocity of 30 Km/hr. As soon as the fly reaches B it immediately turns around and flies towards A, and so on until A and B meet.

a) What will the displacement of the two cyclists and the fly be when all three meet?

b) What will be the distance traveled by the fly?

Homework Equations

x = ut + 0.5at^2
v^2 = u^2 + 2as
v= at+u

The Attempt at a Solution

attempted a method of graphing but failed and attempted fill in variables in equations but failed again

 

[nasu]

There is no acceleration in this problem. The two cyclists move with constant velocities.
Try to find out when will they meet. The equations of motions are just
d1=v1*t
d2=v2*t
with the distances measured from A and B respectively.
What is d1+d2 when they meet?

 

[baba89]

I would approach this problem by first identifying the key information and variables involved. From the given information, we can determine that cyclist A has a displacement of 0 Km, cyclist B has a displacement of 70 Km, and both are traveling towards each other with velocities of 15 Km/hr and 20 Km/hr, respectively. The fly starts at A and travels towards B with a velocity of 30 Km/hr.

Next, I would use the equations of motion to solve for the time it takes for the cyclists to meet. Using the equation x = ut + 0.5at^2, we can set the initial displacement of A to 0 Km and the displacement of B to 70 Km, and solve for t. This gives us a time of 5 hours for the cyclists to meet.

To determine the displacement of the fly when all three meet, we can use the equation x = ut + 0.5at^2 again, but this time with an initial velocity of 30 Km/hr and a time of 5 hours. This gives us a displacement of 150 Km for the fly when all three meet.

For part b, we can use the equation v = at + u to find the distance traveled by the fly. Since the fly starts at A with a velocity of 30 Km/hr and travels for 5 hours, the distance traveled by the fly would be 150 Km.

In conclusion, when all three meet, the displacement of the cyclists will be 35 Km each (since they have traveled 35 Km towards each other) and the displacement of the fly will be 150 Km. The total distance traveled by the fly would be 150 Km.