Gather values for launch velocity and time, as well as the constant for gravity (9.8 m/s^2). In most physics problems, these values should be provided.
Plug the values from Step 1 into the two motion equations for vertical trajectory: Vy = Voy -gt and y = Voy*t-(1/2)g*t^2. In this equation, Vy is velocity, Voy is your launch speed, in either meters per second or feet per second, y is equal to height reached, t is equivalent to time in seconds and g is the gravity constant mentioned above (9.8 m/s^2). If your launch speed is in feet per second, then use the conversion for g, which is 32.15 ft/sec^2.
Calculate both velocity and height using the two equations in Step 2. For example, if my launch speed was 500 meters per second and my time was 25 seconds, when plugged into both equations, the result would be a velocity of 254.75 m/s and a height of 9434.375 meters.
Follow the work for the answers in Step 3:
Vy = Voy - gt
Vy = (500) - (9.81)(25)
Vy = 254.75 m/s
y = Voy*t-(1/2)g*t^2
y = (500)(25)-((1/2)(9.81)(25)^2)
y = 12500 - 3065.625
y = 9434.375 meters