Question

On July 4, 2017, North Korea tested an Inter-Continental Ballistic Missile (ICBM) that ascended to a height of 2802 meters within about 40 minutes. When the missile travels away from the earth, gravitational force and hence the acceleration due to gravity decrease with height. Given the information:

(i) The acceleration due to gravity at a height 'h' above the earth is represented by: G= R² / (R+h)², where 'R' is the radius of the earth and 'g' (-9.8 m/s²) is the acceleration due to gravity at the earth's surface.
(ii) The missile experienced the average between its minimum and maximum accelerations.
(iii) The missile had a single rocket boost.

Answer the following:

A) Determine the average acceleration (deceleration) experienced by the ICBM.
B) Find the initial speed (V₀) and the launch angle of the missile.
C) Calculate the maximum distance the missile could cover if projected at a different angle. Also, determine the new time of flight.

Hints: Use symbols like 'X' for horizontal distance traveled, 'T' for time of flight, and 'a' for acceleration found in (a). Derive an expression for 'V₀' in terms of 'X', 'T', and 'a', then substitute the known values.
For part (C), if you've solved part (B) using symbols, this part should be more straightforward.

Answer 1

To address the student's physics problem, we'd calculate the average deceleration of an ICBM due to changing gravity with height, as well as its initial speed and launch angle using projectile motion equations. For maximum distance and flight time at an optimal angle, the launch angle would be adjusted assuming no air resistance, and the same formulas would be applied.

Step-by-step explanation:

The question involves calculating various parameters associated with the motion of an intercontinental ballistic missile (ICBM). Given the acceleration due to gravity formula G = R² / (R+h)² and using the provided scenario of the missile's test launch, we can find the average acceleration, initial speed, launch angle, maximum distance, and new time of flight for the missile.

To find the average acceleration (deceleration) experienced by the ICBM, we need to calculate the acceleration due to gravity at the surface and at the height reached and then take the average of these two values. The missile ascended to a height of 2802 meters, so we would use this value in the provided gravity equation.

For determining the initial speed (V₀) and launch angle, we could use projectile motion equations and the provided hints to express V₀ in terms of 'X', 'T', and 'a'. After obtaining V₀, the launch angle can be derived from the relationship between horizontal and vertical velocities.

Lastly, to calculate the maximum distance the missile could cover if projected at a different angle, and to determine the new time of flight, we would utilize the formulas for projectile motion, changing the launch angle to the optimal angle for maximum range, which is 45 degrees, provided air resistance is negligible.