When does the collision occur and at what height?

[hannam]

Homework Statement

a ball makes a free-fall with zero initial
velocity and an arrow with 25 m/s initial velocity is thrown to shoot
this ball at the same time. The ball is initially h=38 m higher than the
arrow.
a) Assume no drag force then how long after does this collision occur?
At what height below ball’s initial position does this collision occur?
b) Assume a constant air drag force at any time instant, which is equal
to Drag Force= 2.2 m where m is the mass of object. For this case,
repeat part a). Take g=9.8 m/s2 for both parts of this and other
questions.

Homework Equations

m.g-2,2m=m.a
h=vo.t+1/2gt^2

The Attempt at a Solution

problem is in b part, i solved a.
mg-2,2m=m.a
a=7,6
h=1/2at^2 =3,8t^2

38-3,8t^2= 25.t -1/2.9,8.t^2
there is an quadratic equation now and i think i should have used another formula, I'm not sure. I appreciate your help :)

 

[PhanthomJay]

The quadratic is OK but you forgot to include the air resistance drag force on the arrow.

 

[hannam]

i couldn't decide whether or not to include drag force on the arrow.because, in the question it says "Drag Force= 2.2 m where m is the mass of object" there is no information about the arrow

 

[PhanthomJay]

Balls and arrows are both objects, as I see it..

 

[hannam]

ok i tried that one too but i still have quadratic. how can i find t?

 

[PhanthomJay]

Use quadratic equation, you know, if at^2 +bt + c = 0, then t = [-b +/- sq rt (b^2- 4ac)]/2a?