Question

a woman stands on the bank of a frozen lake with a dog by her side. she skims a bone across the ice at a speed of 3ms. the bone slows down with deceleration 0.4 ms square and the dog chases it with acce;eration 0.6 ms square. how far out from the bank does the dog catch up with the bone

Answer 1

the equation describing the motion of the bone is :
xbone = 3t - 0.2t^2
the equation describing the motion of the dog it
xdog = 0.3t^2

xbone=xdog (when the meet)
3t - 0.2t^2 = 0.3t^2
3t -0.5t^2 = 0
0.5t ( 6 - t) = 0
t = 6

plugging 6 in either xbone or xdog gives you : 10.8