Question

A water balloon is shot into the air so that its height h, in metres, after t seconds is
h = —4.9t^2 + 27t + 2.4

a)How high is the balloon after 1 s?
b)For how long is the balloon more than 30 m high?
c)What is the maximum height reached by the balloon?
d)When will the balloon hit the ground?

Answer 1

a) just sub t=1 into the function

b) set -4.9t^2 + 27t + 2.4 = 30
and solve. You should get two solution for t
The balloon will be above 30 m for all values of t between those two solutions

c) find the vertex, the max height is the h coordinate of the vertex
Use this method:
for y = ax^2 + bx + c, the x of the vertex is -b/(2a)
once you have that value, sub it back in to get the y.
(of course you are dealing with t instead of x, and h instead of y)

d) set —4.9t^2 + 27t + 2.4 = 0 and solve for t
One of the values of t will be negative, that would be an extraneous root.

Answer 2

thnx a lot now i fully understand