Complete Question
A hawk flies in a horizontal arc of radius 12.0 m at constant speed 4.00 m/s. (a) Find its centripetal acceleration. (b) It continues to fly along the same horizontal arc, but increases its speed at the rate of 1.20 m/s 2 . Find the acceleration (magnitude and direction) in this situation at the moment the hawk
Answer:
a
[tex]a_c = 1.33 \ m/s^2[/tex]
b
[tex]a = 1.79 \ m/s^2[/tex]
direction [tex]\theta =45.52^o[/tex] with the horizontal
Explanation:
From the question we are told that
The radius is [tex]r = 12.0 \ m[/tex]
The the speed is [tex]v = 4.00\ m/s[/tex]
The tangential acceleration is [tex]a__{T}} = 1.2 \ m /s^2[/tex]
Generally the centripetal acceleration is mathematically represented as
[tex]a_c = \frac{v^2}{r}[/tex]
=> [tex]a_c = \frac{4^2}{12}[/tex]
=> [tex]a_c = 1.33 \ m/s^2[/tex]
Gnerally the resultant acceleration is mathematically represented as
[tex]a = \sqrt{a_c^2 + a__{T}}^2}[/tex]
=> [tex]a = \sqrt{1.33^2 + 1.20 ^2}[/tex]
=> [tex]a = 1.79 \ m/s^2[/tex]
Generally the direction is mathematically represented as
[tex]\theta = tan ^{-1} [\frac{1.33}{1.20} ][/tex]
[tex]\theta =45.52^o[/tex]
