A football player is moving southward and suddenly turns eastward...

Let the speed of the football player be, $v$.

Then, we can write

$\overset{\to}{v}i = v$\left(- \overset{^}{j}\right)$and$\overset{\to}{v}f = v\left(\overset{^}{i}\right)$.</p><p>We can write force as, </p><p>$\overset{\to}{F} = m\overset{\to}{a} = m\dfrac{\overset{\to}{v}f - \overset{\to}{v}i}{t} = \dfrac{mv}{t}\left(\overset{^}{i} + \overset{^}{j}\right)

Clearly, the direction of the force acting will be towards north-east.