Does the Golf Ball Land Before, In, or After the Lake?

[rasen58]

Homework Statement

Golfer hits a golf ball so that it goes with initial velocity of 40 m/s at angle of 45 degrees. 100 m away is a lake that is 50 m wide. The ball will not bounce or roll when it lands. Where does the ball land?
Before, in, or after the lake.

Homework Equations

Vertical: a = (v-v₀)/t
Horizontal: Δx = v₀t+1/2at²

The Attempt at a Solution

[/B]
I found the time as 2.8 s using the first equation by setting v = 0 (midway in flight), and v₀ = 40sin45
Then I substituted the time into the second equation along with 0 for the acceleration since there is no horizontal acceleration and v₀ = 40cos45. And got 79 m, so the ball lands before the lake.
But apparently the answer is that it lands after the lake.
What did I do wrong?

 

[Bystander]

2.8 s

This is the time for what?

 

[rasen58]

The time to travel halfway.
Oh... I should've used twice that to get the total time. I get 160 m now.
Thanks, my mistake.

 

[Bystander]

Always try to keep in mind what information you get from a calculation, and what information you've been asked to find.

 

[HalfLostAndSearching]

Your approach is correct, but there appears to be an error in your calculation. When you set v = 0 in the first equation, you should use the vertical velocity component, which is v = 40sin45. This will give you a time of approximately 2.2 s. When you substitute this into the second equation, you should use the horizontal velocity component, which is v0 = 40cos45. This will give you a horizontal distance of approximately 88 m, which means the ball lands after the lake.