part 1 of 3: A hawk flies in a horizontal arc of radius 9.9 m at a constant speed of 4.8 m/s. Find its centripetal acceleration. Answer in units of m/s^2.

part 2 of 3: It continues to fly along the same horizontal arc but increases its speed at the rate of 1 m/s^2. Find the magnitude of acceleration under these new conditions. Answer in units of m/s^2.

Part 3 of 3: Find the direction of acceleration relative to the direction of motion under these conditions. Answer between -180 degrees and 180 degrees. Answer in unit of degrees.

(a) Centripetal (or normal)

acceleration is
a(c)= m•v²/R=…
(b) Tangential acceleration
a(τ)= 1 m/s²
a=sqrt{a(c)² +a(τ)²}=...
(c)tanα= a(c)/a(τ)= ..

Part 1 of 3: To find the centripetal acceleration of the hawk, we can use the formula for centripetal acceleration:

Centripetal acceleration (a_c) = (v^2) / r

where v is the speed of the hawk and r is the radius of the arc.

Given that the speed of the hawk is 4.8 m/s and the radius of the arc is 9.9 m, we can substitute these values into the formula:

a_c = (4.8^2) / 9.9

Calculating this expression, we find:

a_c ≈ 2.335 m/s^2

Therefore, the centripetal acceleration of the hawk is approximately 2.335 m/s^2.

Part 2 of 3: In this case, the hawk is still flying along the same horizontal arc but increasing its speed at a rate of 1 m/s^2. This means that the acceleration in addition to the centripetal acceleration will be the rate of change of speed, which is 1 m/s^2.

To find the magnitude of the acceleration under these new conditions, we simply add the centripetal acceleration to the acceleration due to the change in speed:

Magnitude of acceleration = a_c + additional acceleration

Magnitude of acceleration = 2.335 m/s^2 + 1 m/s^2

Magnitude of acceleration ≈ 3.335 m/s^2

Therefore, the magnitude of acceleration under these new conditions is approximately 3.335 m/s^2.

Part 3 of 3: The direction of acceleration relative to the direction of motion can be determined by considering whether the acceleration is in the same direction or opposite direction as the velocity. In this case, as the hawk is increasing its speed, the acceleration is in the same direction as the velocity.

Since the acceleration is in the same direction as the motion, we can consider it to be positive. Therefore, the direction of acceleration relative to the direction of motion is 0 degrees.

Therefore, the direction of acceleration relative to the direction of motion is 0 degrees.