Question

Peregrine falcons are known for their manoeuvring ability. In a BI0 tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at $25\text{m}/\text{s}$?

Short answer

The radius of the turn of the falcon is $42.51\text{m}$.

Step-by-step solution

Step 1. Given information

The falcon can attain a centripetal acceleration of $1.5$ times the free fall acceleration, the speed of the falcon is $25\text{m}/\text{s}$.

The acceleration of free fall of earth is $9.8\text{m}/{\text{s}}^2$.

Step 2. Explanation

The centripetal acceleration of the falcon is,

$a_c=\frac{v^2}{r}\left(\text{I}\right)$

Here, $a_c$is the centripetal acceleration of the falcon, $v$is the liner speed of the falcon, and $r$is the radius of turn.

Substitute $25\text{m}/\text{s}$for $v$and $1.5\left(9.8\text{m}/{\text{s}}^2\right)$ for $a_c$in the above equation to find $r$.

$\left(1.5\left(9.8\text{m}/{\text{s}}^2\right)\right)=\frac{{(25\text{m}/\text{s})}^2}{r}$

$\begin{array}{l}r=42.51\text{m}\\ \approx 43\text{m}\end{array}$

Thus, the radius of the turn of the falcon is $43\text{m}$.