How Does a Hawk's Acceleration Change When Speed Increases in Circular Motion?

[geegeet]

Circular Motion Question!

Homework Statement

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.
Answer in units of m/s2.

Homework Equations

A=V^2/r

The Attempt at a Solution

The Centripital Acceleration is .29m/s2, and I stumped. Any help?

 

[kuruman]

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?

 

[kjohnson]

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.

 

[kuruman]

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.

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.