A playground is surrounded by a fence 2.0 m high. A boy who plays in the
playground kicks a ball vertically upward from a height of 0.2 m with a speed of
10 m/s. How much time does the ball spend above the height of the fence?

Question

A playground is surrounded by a fence 2.0 m high. A boy who plays in the
playground kicks a ball vertically upward from a height of 0.2 m with a speed of
10 m/s. How much time does the ball spend above the height of the fence?

mertsj · Answer

$$-4.9t ^{2}+v _{0}t+s=h$$
$$-4.9t^2+10t+.2>2$$
$$-4.9t^2+10t-1.8>0$$

mertsj · Answer

Set that equal to 0 and solve.  The roots are .2 sec and 1.8 sec .  When t is between those 2 values, the ball will be above the fence.  1.8-.2 = 1.6 sec the ball will be above the fence.