Question

a cheetah is running at a speed of 20.4 m/s in a direction of 67° north of west. find the components of the cheetahs velocity along the following directions. (a) the velocity component due north m/s (b) the velocity component due west m/s

Explanation:

Step1: Recall vector - component formula

For a vector $\vec{v}$ with magnitude $v$ and direction $\theta$ measured from the negative x - axis (west - east axis), the north - south component $v_y$ and west - east component $v_x$ are given by $v_y = v\sin\theta$ and $v_x=-v\cos\theta$. Here, $v = 20.4$ m/s and $\theta = 67^{\circ}$.

Step2: Calculate the north - component

The velocity component due north $v_y$ is given by $v_y=v\sin\theta$. Substitute $v = 20.4$ m/s and $\theta = 67^{\circ}$ into the formula. Since $\sin67^{\circ}\approx0.9205$, then $v_y = 20.4\times0.9205=18.78$ m/s.

Step3: Calculate the west - component

The velocity component due west $v_x$ is given by $v_x=-v\cos\theta$. Since $\cos67^{\circ}\approx0.3907$, then $v_x=- 20.4\times0.3907=-7.99$ m/s. The magnitude of the west - component is what we want, so $|v_x| = 20.4\times0.3907 = 7.99$ m/s.

Answer:

(a) 18.78
(b) 7.99