If a ball is thrown vertically upward from the roof of foot building with a velocity of ft/sec, its height after seconds is What is the maximum height the ball

Question

If a ball is thrown vertically upward from the roof of 48 foot building with a velocity of 80 ft/sec, its height after t seconds is

s(t)= 48+80t-16t^2  What is the maximum height the ball reaches?

 

 

Answer=________________

 

What is the velocity of the ball when it hits the ground (height 0)?

 

Answer=________________

 

Answer 1

1. The maximum height the ball will reach is the vertex of the parabola s(t)=48+80t-16t². first, we need to solve for t. The vertex of any parabola of the form f(x)=ax²+bx+c is found by using x=-b/2a. In this case, x=t, b=80 and a=-16. Substituting we get:

                                 t=-80/((2)(-16)--->t=-80/-32--->t=5/2

Putting this value of t in the original formula will give us the maximum height:

                                s(t)=48+80t-16t²

                                s(5/2)=48+80(5/2)-16(5/2)²

                                s(5/2)=48+200-16(25/4)

                                s(5/2)=248-100

                                s_max=148 feet

2. The instantaneous velocity is the first derivative of the position formula (i.e. s(t)): s'(t)= -32t+80.

    the time, t, is when it hits the ground, so we must solve for t when s(t)=-16t²+80t=48. Using the quadratic formula we get:

 

                (-b±(sq root of b²-4ac))/2a

                (-80±(sq root of 80²-(4)(-16)(48))/((2)(-16))

                (-80±(sq root of 6400+3072))/-32

                (-80±(sq root of 9472))/-32

                (-80±(97.32))/-32

                t=-177.32/-32=5.54 and t=17.32/-32=-.54

Because time has to be positive, t=5.54 sec. Substituting this value into our first derivative equation, we get:

                        s'(t)=-32t+80

                        s'(5.54)=-32(5.54)+80

                        s'(5.54)=-177.28+80

                        s'(5.54)=-97.28 ft/sec

The answer here is -97.28 ft/sec. Why is the answer negative?