A hockey player hits a "slap shot" in practice (with no goalie present) when he is \(15.0 \mathrm{~m}\) directly in front of the net. The net is \(1.20 \mathrm{~m}\) high, and the puck is initially hit at an angle of \(5.00^{\circ}\) above the ice with a speed of \(35.0 \mathrm{~m} / \mathrm{s}\). (a) Determine whether the puck makes it into the net. (b) If it does, determine whether the puck is rising or falling vertically as it crosses the front plane of the net.
THINKING IT THROUGH. First let's make a sketch of the situation using \(x-y\) coordinates, assuming that the puck is at the origin at the time it is hit and showing the net and its height as in Figure 3.19. Note that the launch angle is exaggerated. An angle of \(5.00^{\circ}\) is quite small, but then again, the top of the net is not overly high \((1.20 \mathrm{~m})\).

To determine whether the shot is of goal quality, we need to know whether the puck's trajectory takes it above the net or into the net. That is, what is the puck's height \((y)\) when its horizontal distance is \(x=15.0 \mathrm{~m}\) ? Whether the puck is rising or falling at this horizontal distance depends on when the puck reaches its maximum height. The appropriate equation(s) should provide this information, but keep mind that time is the connecting factor between the \(x\) - and \(y\)-components.

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= 5.00 (exaggerated for clarity) x=0 (launch point) (Ice) 1.20 m x x= 15.0 m y=0