A projectile is fired vertically upward and has a position given by s(t) = −16t2 + 480t + 496 for 0≤t≤31. Complete parts (a)–(e) below.
a. Graph the position function for 0≤t≤23. Choose the correct graph below. Each curve is graphed in a [−4,23,1] by [0,3500,100] window.
b. From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time t=a.
c. Confirm your answer to part (b) by making a table of average velocities to approximate the instantaneous velocity at t=a.
d. For what values of t on the interval [?, ?] is the instantaneous velocity positive (the projectile moves upward)?
e. For what values of t on the interval [?, ?] is the instantaneous velocity negative (the projectile moves downward)?
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