velocity/accerleration of ball question, see if im doing this right.?

Question

i got answers for this question yesterday, i just want to make sure I can solve them right so tell me if what im doing seems correct. And if you correct me try to solve it using one of these formulas:

V=at+V0
(X-X0)= 1/2 (V+V0)t
V^2=V0^2 + 2a (X-X0)
X-X0 = 1/2at^2 + V0t

now...check and see if what I say sounds good

A ball is thrown vertically upward with a velocity of +10.0 m/s.
(a) How high does it rise?
___m

Using V^2=V0^2 + 2a (X-X0)
10^2=0^2 + 2 * 9.8 *x, x = 5.10m

(b) How long does it take to reach its highest point?
___s

Using V=at+V0

10=9.8x, x= 1.0204sec

(c) How long does the ball take to hit the ground after it reaches its highest point?
___s

Heres where I get a bit confused, which equation should I use for this? Would the answer be the exact same? or would it be different a little? I know its pretty much 1 sec

(d) What is its velocity when it returns to the level from which it started?
___m/s

Also help with this one please, I think its just 9.8, thanks

Answer 1

Your answer seems to be correct, I get 9.8 too!

Answer 2

These projectile problems are symmetric no matter what the initial angle: the high point where the vertical velocity reaches zero is exactly halfway through the trajectory in both time and distance, so if you solve either half you've solved the whole thing.

It's easier to start at the midpoint where the projectile begins to fall back to Earth with an acceleration of 9.8 m/s^2. To get the time to fall to the ground, use v=gt and solve for t=v/g=10/9.8=1.02 seconds (if you used 10 m/s^2 for g it would be 1.00 second).

Now you have t so you can solve for s=0.5gt^2=4.9*1.04=5.10 meters (I see you plugged in the initial positions and velocities but in this case you don't need them).

Since the ball's path is symmetric, it will hit the ground at the same speed at which it was thrown, 10 m/s, no math necessary (this is true for bullets fired from a gun, too).

Answer 3

The time reqd for the ball to go up = time reqd for it to come down. Also in the first one, v0=10 and v=0. The rest is ok.