How long will it take the object to reach 9 meters algebra problem

Question

The table below shows the height h(t) in meters of an object that is thrown off the top of a building t seconds after it is thrown

T H(t)

0.5 78.725

1 89

1.5 96.825

2 102.2

2.5 105.125

3 105.6

How long will it take the object to reach 9 meters?

Answer 1

Looking at Larissa's answer of -4.9x²+27.9x+66, this makes sense since gravity = -9.8 m/s² and g/2 = -4.9

The initial upward velocity is v₀ = 27.9 m/s

And the building height is h₀= 66 m

This corresponds to the usual height equation of h(t) = gt²/2 + v₀t + h₀

Answer 2

Hello - we can use excel to fit a quadratic trendline to this data. The resulting equation is y= -4.9x²+27.9x+66.

where x is Time and y is Height. Solving for time when height is 9 meters , gives time of 7.29 seconds