How To Draw A Dog Running
Physics Question about circular motion…?
A merry-go-round is stationary. A dog is running on the ground just outside its circumference, moving with a constant angular speed of 0.710 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the merry-go-round one third of a revolution in front of him. At the instant the dog sees the bone (t = 0), the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of 0.0150 rad/s2.
I know that the first time the dog reaches the bone is 3.05s, but…
(b) The confused dog keeps running and passes the bone. How long after the merry-go-round starts to turn do the dog and the bone draw even with each other for the second time?
the answer is not 91.6s??? how come???
Yes the answer is 91.6s !
We are not both wrong.
In the below equations let d??, v=?, a=d?/dt
d = d? + v?t + ½at²
For the merry-go -around
d =2pi/3+ ½at² (d=0 is at the dog at t=0)
For the dog
d?=vt
d?=0.71t
You let d?=d and you get a quadratic
0=2pi/3 – 0.71t +½at²
If you solve this quadratic equation you get the answers…
t= 3.048 s
and
t= 91.619 s
I used http://www.1728.com/quadratc.htm
Note: He overtakes the bone and then it catches up to him.
