A student estimated based on the video that the ball left my hand 1.56 meters off the ground, and after 0.59 seconds the ball reached the maximum height of 3.26 meters.Use this information to find an equation of the form h=a(t−t1)^2+h1 for the height of the ball, in meters, after t seconds.
Read the problem with attention to answer exactly what was asked.
Use this information to find an equation of the form ...
Form requested h = a(t − t1)2 + h1 for the height of the ball, in meters, after t seconds.
Given: (left hand) initial height is 1.56 meters, so h1 = 1.56
Given: after 0.59 seconds, so (t - t1) = 0.59
To find the equation, we need to find a to substitute its value into the equation.
[Note: Problems have extraneous data sometimes, and this can be confusing. In this case, info that the ball reached (exactly) maximum height is irrelevant. In confusion, one might want to use the parabola vertex properties, which is unnecessary in this case.]
Given: The maximum height (reached) was 3.26 meters, so h = 3.26
Plug in what is given into the equation h = a(t − t1)2 + h1:
3.26 = a(0.59)2 + 1.56 (note that the data given has two decimals for precision)
0.3481 * a = 3.26 - 1.56 (keep precision till the final rounding)
0.3481 * a = 1.70
a ≈ 4.88 (round result of division to two decimals)
We know what we need to "find the equation" now.
The equation of height h of the ball, in meters, after t seconds is
h = 4.88(t) + 1.56
