Missing Part of the Question:
- The time required for the rocket to reach its maximum height
- The maximum height of the rocket
Answer:
a. Time to reach maximum height is 1.37 seconds
b. Maximum Height = 34.1 metres
Explanation:
Given.
H(t) = -4.9t² + 13.4t + 24.9
Solving (a): Time taken to reach maximum height.
A quadratic equation is:
f(x) = ax² + bx + c
Where
a = -4.9
b = 13.4
c = 24.9
This required time is represented by the vertex and is calculated as thus:
t = -b/2a
Substitute values for b and a
t = (-13.4)/(2 * -4.9)
t = -13.4/(-9.8)
t = 13.4/9.8
t = 1.37 (approximated)
Hence the time to reach maximum height is 1.37 seconds
b. Maximum height
Here, we simply substitute 1.37 for t in
H(t) = -4.9t²+ 13.4t + 24.9
Maximum Height = -4.9 * 1.37² + 13.4 * 1.37 + 24.9
Maximum Height = -4.9 * 1.8769 + 13.4 * 1.37 + 24.9
Maximum Height = -9.19681 + 18.358 + 24.9
Maximum Height = 34.06119
Maximum Height = 34.1 metres (approximated)