the time taken by the bumblebee to reach the wheel of the other bike be t therefore we get
S = vt + (1/2)gt^2
S = 32 km = 32 * 10^3 m,v = 11.1 m/s and g = 9.8 m/s^2
or 32 * 10^3 = 11.1t + (1/2) * 9.8 * t^2
or 4.9t^2 + 11.1t - 32 * 10^3 = 0 ----------(1)
solving the above equation we get the time taken by the bumblebee to reach the wheel of the other bike
the motion of the bee and the first bike is shown in the following figure:
In the above figure,u1 is the speed of the first bike,v1 is the speed of the bee towards the first bike and v is the resultant speed.
we know that
v = (v
12 + u
12)
1/2
the total distance the bee travelled is
S1= v * t ----------(2)
the value of v and t is obtained from equations (1) and (2).