本题目来源于试卷: Integral Calculus，类别为 IB数学
[问答题]
A cannonball is fireje(m) 5m *ac*jihie+ed from the top of ao o;yowox6,u;tc1wlwr9h ) g4 tower. The rate of change of the height, h ,9 lcg)w,y; 1wo;wou ooh4tx6r of the cannonball above the ground is modelled by
$h^{\prime}(t)=-4 t+20, \quad t \geq 0$,
where h is in metres and t is the time, in seconds, since the moment the cannonball was fired.
1. Determine the time t at which the cannonball reached its maximum height. __
After one second, the cannonball is 26 metres above the ground.
2. a. Find an expression for h(t) , the height of the cannonball above the ground at time t . __
b. Hence, determine the maximum height reached by the cannonball. __
3. Write down the height of the tower.
4. Calculate the height of the cannonball 4 seconds after it was fired. __
The cannonball hits its target on the ground n seconds after it was fired.
5. Find the value of n . __
6. Determine the total time the cannonball was above the height of the tower. __
A second cannonball is fired from exactly halfway up the tower, with the same projectile motion as the first cannonball.
7. Given that both cannonballs land at the same time, determine the length of time between the first cannonball and the second cannonball being fired. __
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