You are on the roof of your school building \( 60 \,\text{m} \) high. You see your physics teacher walking directly towards the building at \( 2 \,\text{m/sec} \). You wish to throw a ball vertically down at a speed \( 5 \,\text{m/sec} \), so that your teacher may catch it (when teacher is directly below the line of motion of the ball). At what distance (in \( \text{m} \)) from the bottom the building, should your teacher be when you throw the ball? Neglect air resistance and height of the teacher. Take \( g = 10 \,\text{m/sec}^{2} \).
