A test rocket at ground level is fired straight up from rest, with a net upward acceleration of 20 m/s^2. After 4 seconds, the motor turns off, but the rocket continues to coast upward. What maximum elevation does the rocket reach?

486.5 meters

Explanation:

During the acceleration phase, the rocket reaches a height of:

y = y₀ + v₀ t + ½ at²

y = 0 + (0) (4) + ½ (20) (4) ²

y = 160

The velocity it reaches is:

v = at + v₀

v = (20) (4) + 0

v = 80

During free fall, the rocket reaches a maximum height of:

v² = v₀² + 2a (y - y₀)

(0) ² = (80) ² + 2 (-9.8) (y - 160)

y ≈ 486.5

The rocket reaches a maximum height of 486.5 meters (round as needed).

Maximum elevation, h = 160 meters