Answer :
If a ball is thrown to vertically to upward from of the roof of 64 foot building with a velocity of the 32 ft/sec, its height after the t seconds is s(t) = 64 + 32t - 16t^2.
What is velocity ?
velocity is the speed of something in a given direction. It is defined the direction of the movement of the body or the object .
As we know speed is primarily the scalar quantity.
Sol- 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/ s(5/2)=248-100 smax=148 feet
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.
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