A hawk flies in a horizontal arc of radius
15.7 m at a constant speed of 3.8 m/s.
Find its centripetal acceleration.
Answer in units of m/s
2
006 (part 2 of 2) 10.0 points
It continues to fly along the same horizontal arc but increases its speed at the rate of
1.13 m/s
2
.
Find the magnitude of acceleration under
these new conditions.
Answer in units of m/s
To find the centripetal acceleration of the hawk, we can use the formula for centripetal acceleration:
Centripetal acceleration = (velocity squared) / radius
Given:
Radius (r) = 15.7 m
Velocity (v) = 3.8 m/s
Using the formula, we can substitute the given values:
Centripetal acceleration = (3.8 m/s) squared / (15.7 m)
Simplifying the equation:
Centripetal acceleration = 14.44 m^2/s^2 / 15.7 m
Now, to find the magnitude of acceleration under the new conditions where the speed is increasing at a rate of 1.13 m/s^2, we need to calculate the total acceleration.
Total acceleration = Centripetal acceleration + Tangential acceleration
The tangential acceleration is the rate at which the speed is increasing. Given:
Tangential acceleration = 1.13 m/s^2
Substituting the values into the equation:
Total acceleration = Centripetal acceleration + 1.13 m/s^2
Now we can substitute the value of the centripetal acceleration we calculated earlier:
Total acceleration = 14.44 m^2/s^2 / 15.7 m + 1.13 m/s^2
Simplifying the equation:
Total acceleration = 0.9197 m/s^2 + 1.13 m/s^2
Total acceleration = 2.0497 m/s^2
Therefore, the magnitude of acceleration under these new conditions is 2.0497 m/s^2.