SOLUTION: Katie and Josh go mountain climbing. At one point Katie is on a ledge 6 meters directly above Josh. Katie is thirsty so Josh tosses a water bottle straight up to Katie with an init
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Question 1164088: Katie and Josh go mountain climbing. At one point Katie is on a ledge 6 meters directly above Josh. Katie is thirsty so Josh tosses a water bottle straight up to Katie with an initial velocity of +14m/s. The bottle rises and passes Katie on the way up, then it falls back down to her and she catches it as it falls.
A) at what time does the bottle pass Katie going up, and what time does she catch it Answer by ikleyn(52832) (Show Source):
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Katie and Josh go mountain climbing. At one point Katie is on a ledge 6 meters directly above Josh.
Katie is thirsty so Josh tosses a water bottle straight up to Katie with an initial velocity of +14m/s.
The bottle rises and passes Katie on the way up, then it falls back down to her and she catches it as it falls.
A) at what time does the bottle pass Katie going up, and what time does she catch it
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Write the expression for the bottle's height
h(t) = -5t^2 + 14t.
Solve this equation for h(t) = 6
-5t^2 + 14t = 6
5t^2 - 14t + 6 = 0
= = .
= = 0.53 of a second is the time the bottle passes Katie first time moving up,
and
= = 2.27 seconds is the time the bottle passes Katie second time moving down.
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