# Circular Motion of a hawk

1. Nov 25, 2009

### geegeet

Circular Motion Question!!

1. The problem statement, all variables and given/known data

A hawk flies in a horizontal arc of radius 18.3 m at a constant speed of 2.3 m/s.
It continues to fly along the same horizontal arc but increases its speed at the rate of
1.56 m/s2. Find the magnitude of acceleration under these new conditions.

2. Relevant equations

A=V^2/r
3. The attempt at a solution
The Centripital Acceleration is .29m/s2, and I stumped. Any help?

2. Nov 25, 2009

### kuruman

Re: Circular Motion Question!!

When the speed starts increasing, there is a component along the arc (tangential acceleration of 1.56 m/s2) and a component towards the center (centripetal acceleration). These two components are perpendicular to each other. Can you find the magnitude of the total acceleration?

3. Nov 26, 2009

### kjohnson

Re: Circular Motion Question!!

Yes the magnitude is the resulatant of the tangential and normal(centrepital) accelerations, but the magnitude should be a function of time. This is because your tangential acceleration is causing the velocity to increase. Hence even though your tangential acceleration is constant your normal acceleration will increase with time since a=(v^2)/r. So your normal acceleration a(t)=(v(t)^2)/r where v(t) is a linear function that can be determined from the formulas for constant acceleration.

4. Nov 26, 2009

### kuruman

Re: Circular Motion Question!!

Indeed the magnitude is a function of time. However, since the problem does not specify when the magnitude is to be calculated, one can only assume that is at time t = 0, i.e. when the tangential acceleration is "turned on", but before the speed can change appreciably. In my opinion this is not a well-crafted problem.