Question

A football 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 football after 1 second? b) For how long is the football more than 30 m high? c)
What is the maximum height of the football?

Answer 1

a] 24.5; b] 2.8; c] 39.59.

Explanation:

a. after t=1sec:

h(1)=-4.9*1²+27*1+2.4; ⇔h(1)=24.5 [m];

b. more than 30 [m] heigh:

-4.9t²+27t+2.4≥30; ⇔ 4.9t²-27t+27.6≤0; ⇔(t-1.35)(t-4.15)≤0;

Δt≈4.15-1.35=2.8 [sec];

c. maximum height:

h'(t)=-9.7t+27; ⇒ h'(t)=0, ⇒ -9.7(t-2.78)=0; ⇒ t=2.78 [sec], then

`h_(max)=h(2.78)=-4.9*2.78^2+27*2.78+2.4=39.59[m].`