For the ballistic missile aimed to achieve the
maximum range of 15500 km, what is the
maximum altitude reached in the trajectory?
Answer in units of km
7750
To determine the maximum altitude reached by a ballistic missile aimed to achieve a maximum range of 15,500 km, we can use some basic concepts of projectile motion and the equations of motion.
Ballistic missiles are launched at an angle with a certain initial velocity. As the missile ascends, it follows a parabolic trajectory due to the combination of its initial velocity and the gravitational pull of the Earth. At the highest point of its trajectory, the missile reaches its maximum altitude.
To find the maximum altitude, we need to consider the two components of the missile's motion: vertical and horizontal. The gravitational force acts vertically, causing the missile to decelerate until it reaches its highest point.
To calculate the maximum altitude, we can use the following steps:
1. Determine the time of flight: The time it takes for the missile to reach its maximum range can be calculated using the formula: time = range / horizontal velocity. In this case, the range is given as 15,500 km.
2. Calculate the total time of flight: Since the missile follows a symmetric trajectory, the time of flight to reach maximum range is half of the total time of flight. Therefore, the total time of flight is: 2 * time.
3. Calculate the initial vertical velocity component: The initial vertical velocity component can be determined using the formula: Vy = initial velocity * sin(angle). However, the angle is not provided in the question, so we cannot calculate this exact value. So, we'll need to make an assumption about the angle and consider a typical launch angle for a ballistic missile, which is usually between 40 to 60 degrees.
4. Determine the maximum altitude: Using the formula for vertical displacement, we can determine the maximum altitude reached by the missile. The formula is: displacement = Vy * time - 0.5 * g * time^2, where g is the acceleration due to gravity (approximately 9.8 m/s^2). We will convert the displacement to kilometers by dividing by 1000.
By following these steps, you will be able to calculate the maximum altitude reached by the missile with an assumed launch angle. However, without the exact launch angle or more information, we cannot provide an accurate answer.