A cat jumps from a ledge to catch a hummingbird that is hovering above the groun

Question

A cat jumps from a ledge to catch a hummingbird that is hovering above the ground. His jump is filmed and, using frames from the film, his height (in centimeters) is calculated to be the values shown in the table at the corresponding times measured from the start of his jump.

How high is the ledge from which he jumped? centimeters.

Assuming he barely manages to catch the hummingbird at the top of his trajectory, how high was the hummingbird hovering? centimeters.

t (sec) 0 0.2 0.4 0.6 0.8 0.94 h (cm) 63 132 141 120 65 0 A cat jumps from a ledge to catch a hummingbird that is hovering above the ground. His jump is filmed and, using frames from the film, his height (in centimeters) is calculated to be the values shown in the table at the corresponding times measured from the start of his jump. Use Excel's Solver to estimate h0 and v0 and thereby find the least sum squared error parabola of the form h(t)= -490t2 + v0t + h0 How high is the ledge from which he jumped? Assuming he barely manages to catch the hummingbird at the top of his trajectory, how high was the hummingbird hovering?

Explanation / Answer

63cm

521cm

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