Final answer:
The maximum height reached by a projectile, like a rocket, is calculated using the kinematic equation for projectile motion. Assuming an initial vertical velocity of 67.6 m/s and acceleration due to gravity of 9.80 m/s², the maximum height is found to be 233 meters when air resistance is negligible.
Step-by-step explanation:
To find the maximum height (ymax) reached by a rocket, we apply the principles of projectile motion under the condition of constant acceleration due to gravity (9.80 m/s²). The maximum height is achieved when the vertical component of the velocity (Vy) becomes zero. This is the turning point where the projectile stops rising and begins to fall back to the ground.
The equation to calculate the maximum height (h) is derived from the kinematic equation:
v² = v₀² - 2g(y - y₀)
At the maximum height, the final velocity (v) is 0 m/s, so the equation simplifies to:
0 = v₀² - 2gh
Solving for h gives us:
h = v₀² / (2g)
Assuming an initial vertical component of velocity (v₀) is 67.6 m/s, and g (acceleration due to gravity) is 9.80 m/s², the maximum height reached by the projectile, neglecting air resistance, is:
h = (67.6 m/s)² / (2 × 9.80 m/s²) = 233 m
Therefore, the rocket reaches a maximum height of 233 meters.