# SUVAT problem

1. Dec 5, 2015

### Rumplestiltskin

1. The problem statement, all variables and given/known data
What is the velocity of a rugby ball 3.0s after it is kicked vertically upwards with a speed of 16m/s? Give your answer to 2 s.f.
2. Relevant equations
SUVAT
3. The attempt at a solution
s = ?
u = 16
v = ?
a = g = 9.8
t = 3

Erm... v = u + at?
16 + 9.8 x 3 = 45m/s. Incorrect, try again.
...aha! Ball was kicked vertically up. Acceleration is going to be acting against. Not today, physics!
16 - 9.8 x 3 = -13m/s. Incorrect, try again.
Huh. Well, it might be a case of direction. Let's try plain 13m/s. Incorrect, try again.
Okay, let's work out the displacement so we can try v = √2gs. s = 16 x 3 - 0.5 x 9.8 x 3^2 = 3.9m. Nice round number! Must be on to something.
v = √2 x 9.8 x 3.9 = 8.7m/s. Incorrect, try again.
Wait, I'm a doughnut. That's just for free fall. I have a u value. So it's going to be v = √u^2 + 2as.
√16^2 + 2 x 9.8 x 3.9 = 18m/s. Incorrect, try again.
Uh. Oh, g would still be negative. This has got to do it.
√16^2 - 2 x 9.8 x 3.9 = 13m/s. I'm done. SOS.

2. Dec 5, 2015

### haruspex

Looks right to me.

3. Dec 5, 2015

### SteamKing

Staff Emeritus
This is what happens when you throw a bunch of formulas at a problem before thinking it through.

Even rugby balls kicked vertically upward can only rise so high.

What happens when the kicked ball goes up and then starts to come back down within this 3 second interval?

4. Dec 5, 2015

### Rumplestiltskin

Noted.

The velocity reaches 0, and then rises again. How do I tell what point it's at? Could still be rising.

5. Dec 5, 2015

### SteamKing

Staff Emeritus
You don't need to where this occurs, just when it occurs.

6. Dec 5, 2015

### Rumplestiltskin

Huh... just retried and it was accepted this time. That was a headache. Thanks!