Question

a hot air balloon is rising straight up at a constant speed of 7 m/s. when the balloon is 12.0 m/s above the ground, a gun fires a pellet straight up from ground level with an initial speed of 30.0 m/s. Along the paths of the ballon and pellet, there are two places where each of then has the same altitude at the same time. How far above ground are these places?

Answer 1

For the balloon, 
Y = 7 t + 12 
where t is the time the pellet is fired. 
For the pellet, 
Y = 30 t - (g/2) t^2 
= 30 t - 4.9 t^2 


Solve for the two t's when the Y's are equal. 
4.9 t^2 - 23 t +12 = 0 

gravity is 9.8