To find the maximum height reached by the rocket, we can use the equations of motion for vertical motion under constant acceleration.
Given: Initial velocity (v0) = 200 m/s Acceleration due to gravity (g) = 9.8 m/s² (assuming no air resistance)
At the maximum height, the final velocity (vf) will be zero since the rocket momentarily comes to a stop before falling back down. We can use the equation:
vf² = v0² + 2 * g * Δy
where Δy represents the change in height.
Rearranging the equation, we have:
Δy = (vf² - v0²) / (2 * g)
Substituting the known values:
Δy = (0 - 200²) / (2 * 9.8)
Δy = (-40000) / 19.6
Δy ≈ -2040.82 meters
The negative sign indicates that the rocket is below the reference point (ground level) when calculating the change in height. However, in this context, we are interested in the magnitude of the maximum height reached by the rocket, so we take the absolute value:
Maximum height = |Δy| ≈ 2040.82 meters
Therefore, the maximum height reached by the rocket before falling back to Earth, in the absence of air resistance, is approximately 2040.82 meters.