Answer:
t = 0.5 seconds
Step-by-step explanation:
Given formula:
[tex]h=-16t^2+s[/tex]
where:
Dan drops the treat 5 feet above the ground.
Therefore, when t = 0, h = 5 ft.
To find the value of s, substitute these values into the given formula:
[tex]\implies -16(0)^2+s=5[/tex]
[tex]\implies s=5[/tex]
Therefore:
[tex]h=-16t^2+5[/tex]
To calculate how long the treat falls before Lola catches it, substitute h = 1.5 into the formula:
[tex]\implies -16t^2+5=1.5[/tex]
[tex]\implies -16t^2=-3.5[/tex]
[tex]\implies t^2=0.21875[/tex]
[tex]\implies t=\sqrt{0.21875}[/tex]
[tex]\implies t=\pm0.467707173...[/tex]
[tex]\implies t=\pm0.5\; \; \sf (nearest\;tenth)[/tex]
As time is positive, t = 0.5 seconds (nearest tenth) only.
Therefore, it took 0.5 seconds for Lola to catch the treat after it fell.
