help with physics hw please?

Question

Two students are on a balcony 20.8 m above the street. One student throws a ball (ball 1) vertically downward at 10.9 m/s; at the same instant, the other student throws a ball (ball 2) vertically upward at the same speed. The second ball just misses the balcony on the way down.
(a) What is the difference in the two ball's time in the air?
__________ s

(b) What is the velocity of each ball as it strikes the ground?
ball 1 = ________ m/s
ball 2 = ________
m/s
(c) How far apart are the balls 0.800 s after they are thrown?

_________m

Answer 1

First, let's write out the general equation for distance.
d = v1t + 1/2 at^2
d = 0 at t = 0, thus the ground will be defined as -20.8m

a.) Plug in the numbers.
Up ball: -20.8m = 10.9 m/s * t + 1/2 * - 9.8 m/s^2 * t^2
Down ball: -20.8m = -10.9 m/s * t + 1/2 * - 9.8 m/s^2 * t^2

Acceleration is negative, because it's going down, so is the down ball's velocity.

Solve for up ball:
-20.8m = 10.9 m/s * t + 1/2 * - 9.8 m/s^2 * t^2
0 = -4.9t^2 + 10.9t + 20.8
Quadratic formula: t = (-b +/- (b^2 - 4ac)^1/2)/2a
t = (-10.9 +/- (118.81 - -407.68)^1/2) / -9.8
t = 1.112 +/- -2.341
t up ball = 3.453 (ignore negative results)

Solve for down ball:
-20.8m = -10.9 m/s * t + 1/2 * - 9.8 m/s^2 * t^2
0 = -4.9t^2 - 10.9t + 20.8
Quadratic formula: t = (-b +/- (b^2 - 4ac)^1/2)/2a
t = (10.9 +/- (118.81 - -407.68)^1/2) / -9.8
t = -1.112 +/- -2.341
t down ball = 1.229 (ignore negative results)

t up: 3.453
t down: 1.229 (solutions!)

b.) Use Torricelli's equation:
vf^2 = vi^2 + 2ad

Up ball:
vf^2 = 10.9^2 + 2 * -9.8 * -20.8
vf^2 = 118.81 + 407.68
vf^2 = 526.49
vf = 22.945

Now, to save time, realize that the only difference in the equation for Down ball, is that vi is -10.9. When -10.9 is squared, it gives you the same result as 10.9^2, so the down ball hits at the exact same velocity.

vf = 22.945 (solution for both balls)

c.) Use the distance equation again:
Up ball: d = 10.9 m/s * t + 1/2 * - 9.8 m/s^2 * t^2
d = 10.9 m/s * .8 + 1/2 * - 9.8 m/s^2 * .8^2
d = 8.72 - 3.136
d = 5.584

Down ball: d = -10.9 m/s * t + 1/2 * - 9.8 m/s^2 * t^2
d = -10.9 m/s * .8 + 1/2 * - 9.8 m/s^2 * .8^2
d = -8.72 - 3.136
d = -11.856

d (up) - d (down) = 5.584 - -11.856 = 17.44 (solution!)