Question

According to the scientists at NASA's Kennedy Space Center in Houston, Texas, the Space Shuttle' rocket boosters detach at an altitude of 47,549 meters above Earth's surface. As a result of their vertical velocity at the time of separation they continue upward to a maximum altitude of 72,542 meters. What was their velocity at the time of separation? Remember: Gravity is the only acceleration acting on the rocket boosters. Round your answer to the nearest whole number, and enter only that number. Newton's first law can best be described as:(Select ALL or NONE that apply. There may be more than one correct answer.)The law of inertiaThe force needed to accelerate an object

Answer 1

Once the boosters detach they are following an projectile motion; then we can use the following equation to determine its initial velocity;

`v^2_f-v^2_0=2a(y-y_0)`

Now, in this case the initial position is 47549 meters, the final position is 72542 meters, the acceleration is that of the gravity and the final velocity is zero (it has to be zero, otherwise the object will continue going upwards or it will be already falling). Plugging the values we know and solving for the initial velocity we have:

`\begin{gathered} 0^2-v^2_0=2(-9.8)(72542-47549) \\ -v^2_0=-489862.8 \\ v_0=\sqrt[]{489862.8} \\ v_0=699.9 \end{gathered}`

Therefore the initial velocity is 699.9 m/s