math help plz

Question

A rocket is fired upward from a planet . the height in meter after t seconds is given by the function h(t)=-2.3t^2+41t. When will the rocket reach a height of 160 meter. When will it attain its maximum height and what is its maximum height

Answer 1

h(t) = -2.3t² + 41t 

 

It reaches 160 m when h(t) = 160

 

-2.3t² + 41t = 160

 

-2.3t² + 41t - 160 = 0

 

Solve this quadratic equation for t and get 

 

t₁ = 5.77 s (reaches 160 m on the way up)

t₂ = 12.06 s (reaches 160 m again, on the way down)

 

Max height is at the vertex of the height vs. time parabola.

 

t = -41/[2(-2.3)] ≅ 8.91 s

 

h_max = h(8.91) = -2.3(8.91)² + 41(8.91) ≅ 182.7 m