Use the tangent to write

tan(25o) = h1 / 300

and

tan(60o) = (h1 + h2) / 300

Solve for h1 and h2

h1 = 300 tan(tan(25o))

and

h1 + h2 = 300 tan(60o)

Use the last two equations to find h2

h2 = 300 [ tan(60o) - tan(25o) ]

If it takes the balloon 2 minutes (10:00 to 10:02) to climb h2, the the upward speed S is given by

S = h2 / 2 minutes

= 300 [ tan(60o) - tan(25o) ] / (2 * 60) = 3.16 m/sec