A superhero leaps from a building to capture a villain. The data from his leap i

Question

A superhero leaps from a building to capture a villain. The data from his leap is shown below Circle the type of function that best models this data. Use a graphing calculator to perform the regression for the best-fit equation. Write the resulting equation below, rounding to the nearest hundredth. Determine the initial velocity of the superhero's jump and the height of the building. Round to the nearest hundredth. Calculate how many seconds it takes for the superhero to land on the ground (assume no flying powers used). Show your work and round to the nearest hundredth.

Explanation / Answer

The Best fit curve is Quadratic ( parabola)

The obtained equation for the trend line is
x= -16.27 t2 +51.45t + 78.58 ,

this gives a R2= 0.9999 which is almost perfect.

The velocity is dx/dt = -32.54 t +51.45 at time 0, v = 51.45 ft/s

the height of the building is when x = 0, y = 78.52 m

to find the time when it reach the ground simply y = 0, which gives you 4.28s

to summarize, V = 51.446 ft/s, height building = 78.52 ft, time to reach ground = 4.28s

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