QuestionA ball is thrown with a velocity of $41 \mathrm{ft/s}$. Its height after $t$ seconds is $y=41t-22t^2$. Find average velocity for $t=2$ over 0.01, 0.005, 0.002, and 0.001 seconds, then determine instantaneous velocity at $t=2$.

Studdy Solution
As $\Delta t$ approaches $0$, the term $\frac{6}{\Delta t}$ approaches infinity, and the term $22\Delta t$ approaches $0$. Therefore, the instantaneous velocity is$$\text{Instantaneous velocity} =41 -0 + \infty = \infty$$The instantaneous velocity when $t=2$ is infinity.