#v_0 = 20 m/s#
#h_0 = 60 m#
#h = h_0 + v_{0y} t - g t^2/2#
#"Take g = 10 m/s² for simplicity (gravity constant)"#
#"(normally it is 9.81 m/s²)"#
#=> 75 = 60 + v_{0y} * 1 - 10.0 * 1^2 / 2#
#=> 15 = v_{0y} - 5.0#
#=> 20.0 = v_{0y}#
#=> 80 = 60 + v_{0y} * 2 - 10.0 * 2^2 / 2#
#=> 20 = 2 * v_{0y} - 20.0#
#=> v_{0y} = 20 m/s#
#v_{0y} = v_0 => " The projectile is fired vertically upwards."#
#"So the data in the table are consistent with the physical"#
#"laws of falling under gravity."#
#"So the formula is : "#
#d = 60 + 20*t - 5*t^2#
#"Now the projectile reaches the ground when d=0 :"#
#0 = 60 + 20*t - 5*t^2#
#"This is a quadratic equation that can be simplified by dividing"#
#"both sides through -5 :"#
# t^2 - 4 t - 12 = 0#
#"The discriminant is : "4^2 + 12*4 = 64 = 8^2#
#=> t = (4 pm 8)/2 = cancel(-2) or 6#
#"(t = -2 is not possible physically so t = 6 remains)"#
#=> t = 6" seconds"#
#"Note that the graph is a parabole."#
