Question

a Lady bug with a velocity of 10.0mm/s [W] crawls on a chair that is being pulled [50 N of W] at 40.mm/s. what is the velocity of the ladybug, relative to the ground?

Answer 1

a Lady bug with a velocity of $10.0\mathrm{mm / s}$ [W] crawls on a chair that is being pulled [50 N of W] at 40.mm/s. what is the velocity of the ladybug, relative to the ground?

We will used a Galilean addition of velocities:

$$\vec {V} = \vec {V _ {0}} + \vec {V ^ {\prime}}$$

where $\vec{V}$ the velocity of the ladybug, relative to the ground;

$\vec{V^{\prime}}$ - the velocity of a chair;

$\vec{V}^{\prime}$ - the velocity of the ladybug with respect to the chair (moving coordinate system););

From the law of cosines:

$$\begin{array}{l} V ^ {2} = V _ {0} ^ {2} + V ^ {\prime 2} - 2 V _ {0} V ^ {\prime} \cos \alpha \\ = 1 0 ^ {2} + 4 0 ^ {2} + 2 * 1 0 * 4 0 \cos (9 0 - 5 0) = 1 0 0 + 1 6 0 0 + 8 0 0 * \cos (4 0) = 2 3 1 3 \\ \end{array}$$

$\mathrm{V} = 48.09 \mathrm{~mm} / \mathrm{s}$