Since this question does not have a physics tag, I will answer assuming no physics background. That being said it is easiest to answer part b first. The x value of the vertex of any parabola can be found by evaluating -b/2a where a = -4.9 and b = 24.5.
Substitute and Evaluate:
-b/2a = -24.5/(2 * -4.9) = 2.5 s This means the cannonball will reach its highest point after 0.1 seconds.
Now that we know when the cannonball is at its highest, we can find the height at that time. Simply evaluate h(2.5).
h(2.5) = -4.9*(2.5)2 + 24.5*(2.5) + 9.7 = 40.325 m
For part c, we want to find when our function is zero. In other words we want to find the zeros of our function. To do this we will evaluate the quadratic equation where: a = -4.9, b = 24.5, and c = 9.7
Evaluate Quadratic:
When you do this you will get two answers: t = -0.369 or t = 5.369. Since our variable is in time, the first time value does not make sense, so the answer must be t = 5.369 s when the cannonball hits the ground.
a) 40.325 m
b) 2.5 s
c) 5.369 s
