what is the maximum horizontal distance traveled by the soccer ball?

[Jessie]

a soccer player kicks a ball into the air at an angle of 31 degrees above the horizontal and it lands at the same height from which it was kicked. The intial velocity of the ball is 35m/s.

also: What is the maximum height reached by the soccer ball?
for this one -the mximum height question- I did

sin31(35) = 18 is this one at least right? The first question i'm completely lost on.. HELP!

 

[Dozo]

It has a vertical velocity of 35*sin(31). The time till it hits the ground again is the time till it has a velocity of -35*sin(31). The velocity difference is therefore 2*35*sin(31). At an acceleration of g = 9.8 m/s^2 this takes a time t = 2*35*sin(31)/9.8.

The maximum height is 1/2 a t^2 = 1/2 * g t^2. Where t is have the one above.

The horizontal velocity is 35*cos(31). Travelling a this speed for a time t gives a distance d = v * t = 35*cos(31) * 2*35*sin(31)/9.8 = 73 m.