Problema Solution
In the video, I drop a ball off a three-story balcony. We know that objects in freefall follow the equation for height h, in meters, h = -4.9t^2 + c, where t is time in seconds, and c is the initial height. A student timed the drop at 1.3 seconds.
Use this to determine the height from which the ball was dropped, to at least 2 decimal places.
Answer provided by our tutors
h(t) = -4.9t^2 + c, where t is time in seconds, and c is the initial height.
the time of the drop is t = 1.3s then h(1.3) = 0
h(1.3) = - 4.9*(1.3)^2 + c
- 4.9*(1.3)^2 + c = 0
by solving the equation we find
c = 8.281
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h(t) = -4.9t^2 + 8.281
we want to determine the height from which the ball was dropped
for t = 0 the begining moment the height of the ball dropped is h(0)
h(0) = -4.9*0^2 + 8.281 = 8.281 = 8.28 meters is the height from which the ball was dropped.