Chapter 1.8, Problem 34E

Technology Exercises

Position of a Ball A ball thrown straight up into the air has height $s\left(t\right)=102t-16t^2$ feet after $t$ seconds.

(a) Display the graphs of $s\left(t\right)$ and $s\text{'}\left(t\right)$ in the window $\left[0,7\right]$ by $\left[-100,200\right]$. Use these graphs to answer the remaining questions.

(b) How high is the ball after $2$ seconds?

(c) When, during descent, is the height $110$ feet?

(d) What is the velocity after $6$ seconds?

(e) When is the velocity $70$ feet per second?

(f) How fast is the ball traveling when it hits the ground?