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/s2. Find the acceleration (magnitude and direction) in this situation at the moment the hawk’s speed is 4.00 m/s.

Answer 1

Answer:

a) $a_c= 1.33 m/s^2$

b) a= 1.79 m/s²

   θ = 41.98⁰

Explanation:

arc radius  = 12 m

constant speed = 4.00 m/s

(a) centripetal acceleration

     $a_c=\frac{v^2}{R}$

     $a_c=\frac{4^2}{12}$

                  = 1.33 m/s²

(b) now we have given

        $a_t= \ 1.20 m/s^2$

        now,

         $a=\sqrt{a^2_c+ a^2_t}$

         $a=\sqrt{1.33^2+ 1.20^2}$

            a= 1.79 m/s²

 direction

$\theta = tan^{-1}(\frac{a_t}{a_r} )$

$\theta = tan^{-1}(\frac{1.2}{1.33} )$

     θ = 41.98⁰