A red ball is thrown down with an initial speed of 1.2 m/s from a height of 25 meters above the ground. Then, 0.6 seconds after the red ball is thrown, a blue ball is thrown upward with an initial speed of 22.9 m/s, from a height of 0.8 meters above the ground. The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9.81 m/s2.

I need help on this one..
do i set heights equal?
If so..what equation do i use? Thank You
How long after the red ball is thrown are the two balls in the air at the same height?

To find out how long after the red ball is thrown are the two balls in the air at the same height, you can equate the height equations for the two balls and solve for time.

The height equation for the red ball can be expressed as:

h_r = h_0r + v_0r*t - (1/2) * g * t^2

Where:
h_r is the height of the red ball at any given time t
h_0r is the initial height of the red ball (25 meters)
v_0r is the initial velocity of the red ball (1.2 m/s)
g is the acceleration due to gravity (9.81 m/s^2)
t is the time elapsed

The height equation for the blue ball can be expressed as:

h_b = h_0b + v_0b*t + (1/2) * g * t^2

Where:
h_b is the height of the blue ball at any given time t
h_0b is the initial height of the blue ball (0.8 meters)
v_0b is the initial velocity of the blue ball (22.9 m/s)
g is the acceleration due to gravity (9.81 m/s^2)
t is the time elapsed

To find the time when the two balls are at the same height, we need to set h_r equal to h_b and solve for t:

h_r = h_b
h_0r + v_0r*t - (1/2) * g * t^2 = h_0b + v_0b*t + (1/2) * g * t^2

Simplifying the equation:

(h_0r - h_0b) + (v_0r - v_0b)*t - g*t^2 = 0

Now we have a quadratic equation in terms of t. We can use the quadratic formula to solve for t:

t = (-b ± √(b^2 - 4ac)) / (2a)

Where a = -g, b = (v_0r - v_0b), and c = (h_0r - h_0b)

Plug in the values for a, b, and c, and solve for t. Note that you will have two solutions, one positive and one negative. The positive solution is the time after the red ball is thrown when the two balls are at the same height.

I hope this helps! Let me know if you have any further questions.