Math CentralQuandaries & Queries


Question from san, a student:

A football player attempts a field goal by kicking the football. The ball follows
the path modelled by the equation h= -4.9^2+10t+3, where h is the height of the
ball above the ground in metres, and t is the time since the ball was kicked
in seconds.
*the ball must clear the uprights for the field goal to count. The uprights are approximately
5 m high. How long does the ball stay above 5 m in height?

Hi San,

This question might seem strange as it doesn't tell you how far the ball is from the goal posts. You have to kick the ball high enough to clear the bar but you also have to give it enough forward force that it will be above 5 metres when it gets to the uprights. This question is only about the height above the ground.

The height h in metres, t seconds after the ball is kicked is

h= -4.9t2+10t+3

The ball will be at a height of 5 metres twice, once on the way up and once on the way down. These two times are the solution of

5 = -4.9t2+10t+3

Solve this equation for t and find the difference between the two values.


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