Question

The height of a projectile launched into the air can be mideled by: h(t) = -4t^2 + 50t + 5 where h(t) is the height of the ball in feet after t seconds

a) find h(0) a give the real world meaning for this value
b) what is the height of the projectile when t = 4 seconds?
c) when will the projectile reach a height of 100 feet?
d) how long will it take for the projectile to reach the ground?

Answer 1

\(\bf h(t) = -4t^2 + 50t + 5\\ \quad \\ \quad \\

{\color{blue}{ a}}\qquad h({\color{red}{ 0}}) = -4({\color{red}{ 0}})^2 + 50({\color{red}{ 0}}) + 5\\ \quad \\
{\color{blue}{ b}}\qquad t=4\qquad h({\color{red}{ 4}}) = -4({\color{red}{ 4}})^2 + 50({\color{red}{ 4}}) + 5\\ \quad \\
{\color{blue}{ c}}\qquad y=100\qquad {\color{red}{ 100}} = -4t^2 + 50t + 5\\ \quad \\
{\color{blue}{d}}\qquad y=0\qquad {\color{red}{ 0}} = -4t^2 + 50t + 5\)

for c) and d)
solve for "t"