a) The constant term 5 represents the y-intercept of the equation on the graph.
b) The linear term 100t represents factors such as air resistance.
c) The negative quadratic term -16t² indicates that certain nonlinear effects, like air resistance or drag, have a stronger impact as the rocket's velocity increases
d) The rocket hits the ground at t = 6.3 sec.
e) The appropriate domain of the function is (0,6.3).
What is a parabola?
Given the parabolic equation
h(t) = 5 + 100t - 16t²
a)The constant term 5 represents the y-intercept of the equation on the graph.
b) The linear term 100t represents factors that increase or decrease linearly with velocity such as air resistance or other factors influencing the motion of the rocket.
c) The negative quadratic term -16t² indicates that certain nonlinear effects, like air resistance or drag, have a stronger impact as the rocket's velocity increases.As the rocket accelerates, the quadratic term captures the increasing influence of these forces, affecting the overall behavior of the rocket's trajectory.
d) When rocket hits the ground h(t) = 0
So,
5 + 100t - 16t² = 0
Solve using quadratic formula
t = (-b +-√b² - 4ac)/2a
where
a = -16, b = 100, c = 5
t = (-100 +-√100² - 4(-16)(5))/2(-16)
t =( -100 +-√10000 + 320)/-32
= (-100 +- 101.6)/-32
= -100 + 101.6/-32 or -100 - 101.6/-32
= -0.05 s or 6.3 s
Since time cannot be negative, -0.05 s does not apply.
The rocket hits the ground at t = 6.3 sec.
e) The appropriate domain of the function is (0,6.3). That is from 0 to 6.3. As negative value is not practicable in this sense.