Final answer:
The maximum height of a rocket fired at an angle of 80 degrees with an initial speed of 110 meters per second is approximately 598.73 meters, which is option B.
Step-by-step explanation:
To find the maximum height of a rocket (miswritten as 'rooket' and 'rock' in the question) fired at an angle of 80 degrees from the ground with an initial speed of 110 meters per second, we start by calculating the vertical component of the initial velocity. The maximum height can be determined using the kinematic equation for projectile motion:
h = (v0y2) / (2g), where v0y is the initial vertical speed and g is the acceleration due to gravity (9.81 m/s2).
The vertical component of the initial velocity is calculated as:
v0y = v0 × sin(θ)
v0y = 110 m/s × sin(80°) = 110 m/s × 0.9848 ≈ 108.33 m/s
Substitute v0y into the equation for maximum height:
h = (108.33 m/s)2 / (2 × 9.81 m/s2) ≈ 598.73 meters
Therefore, the maximum height of the rocket is approximately 598.73 meters which corresponds to option B.