A water balloon is catapulted into the air so that its height h, in metres, after t seconds is h=-4.9t2 +27t+2.4
a) How high is the balloon after 1 second?
b) For how long is the balloon more than 30 m high?
c) What is the maximum height of the balloon?
d) When will the balloon burst as it hits the ground?
a) just replace the t with 1 in
h=-4.9t2 +27t+2.4
b) your function is represented by a downwards parabola, so let's see
when -4.9t2 +27t+2.4 = 30
4.9t^2 - 27t +27.6 = 0
by the formula , t = (27 ± √188.04)/9.8 = appr 1.36 or 4.15 sec
So it would be above those times, or for a duration of 2.8 seconds
c) set
-4.9t^2 + 27t + 2.4 = 0
and solve for t. Obviously reject the negative answer