Question

A soccer ball is kicked at a velocity of 25 meters per second. The following table shows the horizontal distance (in meters) at different angles of elevation (in degrees), ignoring wind resistance.

Angle of Elevation Distance Traveled
15 31.9
25 48.8
30 55.5
45 63.8
50 62.8
55 59.9
60 55.5
70 41.0
Using a graphing or online calculator, graph this set of data on a scatter plot for reference. Then, in two or more complete sentences, explain why a quadratic function should be used to model this set of data.

Answer 1

13.2m

Explanation:

the initial vertical velocity of the ball is 25 sin 40 = 16.1m/s

since gravity reduces the vertical velocity of objects by 9.8m/s/s, this ball will reach max altitude in a time of

time = 16.1m/s / 9.8m/s/s = 1.6s

the max height is equivalent to the height an object will fall in 1.6s, so we have

height =1/2 g t^2 = 1/2 x 9.8m/s/s x (1.6s)^2 = 13.2m