If h(t) represents the height of an object above ground level at time t and h(t) is given by h(t)=−16t^2+11t+1 find the height of the object at the time when the speed is zero. h(t)=

Question

If h(t) represents the height of an object above ground level at time t and h(t) is given by  h(t)=−16t^2+11t+1  find the height of the object at the time when the speed is zero. h(t)=

campbell_st · Answer

2 methods

1. calculus... get the 1st derivative and solve for t, substitute it into the equation to find the max height when speed is zero. 



2. for a quadratic find the vertex, which is on the line of symmetry

$$h(t) = at^2 +bt + c$$

find the line of symmetry 

$$t = \frac{-b}{2a}$$

in your question a = -16 and b = 11

this is the time when speed is zero... 

substitute it into the original equation to get the height ( line of symmetry, height) is the vertex.

campbell_st · Answer

both methods give the same answer