Answer: B) 14.7 meters
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Explanation:
The bottle cap is a projectile, so we'll use the aptly named projectile formula
That formula (the meters version of it anyway) is approximately
h = -4.9t^2 + v*t + s
where,
- t = elapsed time in seconds
- h = height at time t
- v = starting velocity
- s = starting height
We'll assume that s = 0, though realistically it's probably going to be a bit larger than this (since the person is holding it above the ground). For the sake of simplicity, we'll stick with s = 0.
We're told that the initial velocity is 17 m/s, which means v = 17.
All of that means the formula mentioned earlier updates into this:
h = -4.9t^2 + 17t
If we were to graph this, or apply the -b/(2a) formula, then you should find that the vertex occurs when t = 1.73469 approximately.
Plug this into the equation we found to get...
h = -4.9t^2 + 17t
h = -4.9(1.73469)^2 + 17(1.73469)
h = 14.7449
h = 14.7
The bottle cap will reach a peak height of approximately 14.7 meters and does so at around the 1.7 second mark. The total flight time is approximately 2*1.7 = 3.4 seconds. This all assumes that the starting height and ending height are both 0 meters off the ground.
