Answer:
The number of seconds it takes for the ball to reach the maximum height is 0.5102
Step-by-step explanation:
we have
[tex]h(t)=-4.9t^{2}+5t+3[/tex]
where
h(t) is the height in meters above the ground
t is the time in seconds
This is a vertical parabola open downward
The vertex is a maximum
The number of seconds it takes for the ball to reach the maximum height is equal to the x-coordinate of the vertex
Convert the given function to vertex form
[tex]h(t)=-4.9t^{2}+5t+3[/tex]
Factor -4.9
Complete the squares
[tex]h(t)=-4.9(t^{2}-\frac{5}{4.9}t+\frac{5^2}{9.8^2})+3++\frac{5^2}{9.8^2}(4.9)[/tex]
[tex]h(t)=-4.9(t^{2}-\frac{5}{4.9}t+\frac{5^2}{9.8^2})+3+1.2755[/tex]
[tex]h(t)=-4.9(t^{2}-\frac{5}{4.9}t+\frac{5^2}{9.8^2})+4.2755[/tex]
Rewrite as perfect squares
[tex]h(t)=-4.9(t-\frac{5}{9.8})^{2}+4.2755[/tex]
The vertex is the point [tex](\frac{5}{9.8},4.2755)[/tex]
Divide the fraction
[tex](0.5102,4.2755)[/tex]
therefore
The number of seconds it takes for the ball to reach the maximum height is 0.5102
