Final answer:
To calculate the maximum height of the rocket, we convert the initial velocity to meters per second and use the kinematic equation for vertical motion under the influence of gravity. The rocket reaches a maximum height of approximately 6.37 meters.
Step-by-step explanation:
Calculating the Maximum Height of the Rocket
To determine the height that the rocket reaches at the point where its velocity is zero, we utilize the kinematic equation for vertical motion under the influence of gravity, which is:
vf^2 = vi^2 - 2*g*h
where vf is the final velocity (0 m/s at the highest point), vi is the initial velocity (25 mph, but we will convert it to meters per second), g is the acceleration due to gravity (9.81 m/s^2), and h is the height.
Firstly, we convert the velocity from mph to m/s:
25 mph ≈ 11.176 m/s
Now, we plug the values into the equation and solve for h:
0 = (11.176 m/s)^2 - 2*(9.81 m/s^2)*h
0 = 124.912 - 19.62*h
h = 124.912 / 19.62
h ≈ 6.368 meters
The rocket reaches a maximum height of approximately 6.37 meters.