APFIVE Initial Velocity and Time to Maximum Height
A researcher records the height of a projectile as $$h(t)= -9.8*t^2+30*t+2$$ meters, where $$t$$ is the time in seconds. What would happen if the initial launch speed is increased by 5 m/s, modifying the height function to $$h(t)= -9.8*t^2+35*t+2$$; how does the time at which maximum height is reached change?
| t (s) | h(t) Original (m) | h(t) Modified (m) |
|---|---|---|
| 0 | 2 | 2 |
| 1 | 22.2 | 26.2 |
| 1.5 | 24.65 | 27.45 |
| 2 | 17.4 | 24.4 |
A
It remains unchanged because the acceleration is constant.
B
It becomes unpredictable due to nonlinear effects.
C
It increases, delaying the vertex to approximately 1.79 seconds.
D
It decreases, with the maximum height occurring sooner.
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