Question

question 3 (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 magnitude of the pucks final velocity at time t = 0.50 s. a. 2.8 m/s b. 1.4 m/s c. 2.2 m/s d. 3.0 m/s

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 $t = 0.50\ s$.
$v_x=v_{0x}+a_x t=1.0 + 2.0\times0.50=1.0 + 1.0=2.0\ m/s$

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 $t = 0.50\ s$.
$v_y=v_{0y}+a_y t=2.0+( - 2.0)\times0.50=2.0 - 1.0 = 1.0\ m/s$

Step3: Calculate the magnitude of the final velocity

Use the formula $v=\sqrt{v_x^{2}+v_y^{2}}$.
$v=\sqrt{(2.0)^2+(1.0)^2}=\sqrt{4.0 + 1.0}=\sqrt{5.0}\approx2.2\ m/s$

Answer:

C. 2.2 m/s