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Super! As the surface is perfectly smooth, there is no friction anymore. So, the net force on the football is \(0\). If the net force is \(0\), from \(F = m a\), the acceleration \(a = \frac{F}{m} = 0\). As \(a = 0\), the ball's velocity doesn't change.
Force is a vector object. So, like velocity and acceleration, it also has x- and y-components. The equations are \(F_x = m a_x\) and \(F_y = m a_y\).
As shown here, a force of \(10 \, \mathrm{N}\) is being exerted on a block of mass \(4 \, \mathrm{kg}\). The force is being applied at an angle of \(30 ^{\circ}\). What are \(a_x, a_y\)?
  • \(a_x = \frac{10}{4}, \, a_y = 0\)
  • \(a_x = 0, \, a_y = \frac{10}{4}\)
  • \(a_x = \frac{10 \cos 30}{4}, \, a_y = \frac{10 \sin 30}{4}\)
  • \(a_x = \frac{10 \sin 30}{4}, \, a_y = \frac{10 \cos 30}{4}\)