The height h metres of a ball at time t seconds after it is thrown up in the air is given by the expression: h = 1 + 15t - 5t^2
(i) find the times at which the height is 11m.
(ii) Use your calculator to find the time at which the ball hits the ground.
(iii) What is the greatest height the ball reaches?
+128474 (i) -5t^2 + 15t + 1 = 11
-5t^2 + 15t - 10 = 0 divide through by -5
t^2 - 3t + 2 = 0 factor
(t - 2) ( t - 1) = 0
At 11m at 1sec and 2 sec
(ii) -5t^2 + 15t + 1 = 0
5t^2 - 15t - 1 = 0
Hits the ground at ≈ 3.06 sec (from WolframAlpha)
(iii) Greatest height reached at time (-15) / (2 (-5) ) = 15/10 = 1.5 sec
Max ht = -5(1.5)^2 + 15 (1.5) + 1 = 12.25 m
