(A.)

A hawk flies in a horizontal arc of radius
13.4 m at a constant speed of 4.5 m/s.
Find its centripetal acceleration.
Answer in units of m/s2.

(B.)
It continues to fly along the same horizon-
tal arc but increases its speed at the rate of
1.45 m/s2.
Find the magnitude of acceleration under
these new conditions.
Answer in units of m/s2.

(A.) To find the centripetal acceleration of the hawk, we can use the formula:

centripetal acceleration = (velocity^2) / radius

In this case, the velocity of the hawk is given as 4.5 m/s and the radius of the arc is given as 13.4 m. Plugging these values into the formula, we get:

centripetal acceleration = (4.5 m/s)^2 / 13.4 m

Calculating this, we get a centripetal acceleration of approximately 1.521 m/s^2.

(B.) To find the magnitude of acceleration under the new conditions, we need to consider both the centripetal acceleration and the increase in speed. The centripetal acceleration remains the same as in part (A) since the radius of the arc has not changed. However, now we also have an additional acceleration due to the increase in speed.

To calculate the additional acceleration, we can simply use the given rate of increase:

additional acceleration = 1.45 m/s^2

We can then find the magnitude of acceleration by taking the square root of the sum of the squares of the centripetal acceleration and the additional acceleration:

magnitude of acceleration = sqrt((centripetal acceleration)^2 + (additional acceleration)^2)

Plugging in the values, we get:

magnitude of acceleration = sqrt((1.521 m/s^2)^2 + (1.45 m/s^2)^2)

Calculating this, we get a magnitude of acceleration of approximately 2.074 m/s^2.