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(problem reference 3 - 1) a puck is moving on a frictionless air hockey table. relative to an x,y coordinate system at time t0 = 0 s, the x components of the pucks initial velocity and acceleration are v0x = + 1.0 m/s and ax = +2.0 m/s². the y - components of the pucks initial velocity and acceleration are v0y = + 2.0 m/s and ay = -2.0 m/s².
find the direction of the pucks final velocity at time t = 0.50 s. specify the direction relative to the +x axis
a. 63°
b. 72°
c. 45°
d. 27°

Explanation:

Step1: Find x - component of final velocity

Use the equation $v_x=v_{0x}+a_x t$. Given $v_{0x} = 1.0\ m/s$, $a_x=2.0\ m/s^2$ and $t = 0.50\ s$. Then $v_x=1.0+2.0\times0.50=1.0 + 1.0=2.0\ m/s$.

Step2: Find y - component of final velocity

Use the equation $v_y=v_{0y}+a_y t$. Given $v_{0y}=2.0\ m/s$, $a_y=- 2.0\ m/s^2$ and $t = 0.50\ s$. Then $v_y=2.0+( - 2.0)\times0.50=2.0 - 1.0 = 1.0\ m/s$.

Step3: Find the direction of the velocity

Use the formula $\theta=\arctan(\frac{v_y}{v_x})$. Substitute $v_x = 2.0\ m/s$ and $v_y=1.0\ m/s$ into the formula. $\theta=\arctan(\frac{1.0}{2.0})\approx27^{\circ}$.

Answer:

d. $27^{\circ}$