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A rock is thrown upward with a velocity of 14 meters per second from the top of a 35 meter high cliff,
and it misses the cliff on the way back down. When will the rock be 3 meters from ground level?
Round your answer to two decimal places.
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The function describing the height over the base of the cliff is
h(t) = -5t^2 + 14t + 35.
The rock will be 3 meters from ground level when h = 3.
So, to find the relevant time t, you should solve this equation
-5t^2 + 14t + 35 = 3.
Simplify
-5t^2 + 14t + 32 = 0
5t^2 - 14t - 32 = 0
and find t using the quadratic formula
t = = .
Use the positive root and reject the negative one.
ANSWER. t = = 4.29 seconds (rounded).
Solved.
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In this site, there is a bunch of lessons on a projectile thrown/shot/launched vertically up
- Introductory lesson on a projectile thrown-shot-launched vertically up
- Problem on a projectile moving vertically up and down
- Problem on an arrow shot vertically upward
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Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn on how to solve this type of problems once and for all.