Question

a rocket test flight takes off, beginning at rest, from kennedy space center with an initial upward acceleration of 4.00 m/s². at a height of 1.00 x 10³ m above the ground the rocket runs out of fuel and the booster immediately shuts of. what is the rocket's velocity in m/s at this point?

Answer 1

The rocket's velocity when it reaches a height of 1.00 x 10³ m, starting from rest and accelerating at 4.00 m/s², is approximately 89.44 m/s.

Step-by-step explanation:

The student asked: At what velocity does a rocket, starting at rest and accelerating upward at 4.00 m/s², reach a height of 1.00 x 10³ m?

To solve this, we utilize the kinematic equation which relates initial velocity (v0), final velocity (v), acceleration (a), and displacement (d): v² = v0² + 2ad. Here, the initial velocity v0 is 0 (starting at rest), the acceleration a is 4.00 m/s², and the displacement d is 1.00 x 10³ m (the height).

Plugging in the values, we get: v² = 0 + 2 * 4.00 m/s² * 1.00 x 10³ m, which simplifies to: v² = 8.00 * 10³ m²/s². Taking the square root of both sides, we find: v = √(8.00 * 10³) m/s. Thus, v ≈ 89.44 m/s.

The rocket's velocity at 1.00 x 10³ m is approximately 89.44 m/s.