Projectile Motion problem?

Question

I have a physics problem, seems simple but I am getting a different answer than the book.

Problem : A ball is kicked at 15m/s horizontally on a 45 deg hill. In how much time will the ball land on the ground?

Books answer is 5.1 sec. I don't know how they get this answer.

Thanks for the help in advance.

Answer 1

The ball will travel horizontally at x(t)=15*t
it will fall at y(t)=-.5*g*t^2

Of course, the hill falls away at
y(t)=-15*t
so when
.5*g*t^2=15*t
the ball makes contact with the hill. Note that t=0 is a solution since the ball was kicked from ground level.

The second root is
t=30/9.8

I get 3.1 sec. Maybe a typo in the book?

j