A James Bond villain fires an intercontinental ballistic missile initially trave

Question

A James Bond villain fires an intercontinental ballistic missile initially traveling at 4 km/sec from the surface of the ocean at an angle of 40.
a. (10 points) Assuming constant acceleration due to gravity and neglecting air resistance, how high does the missile get at the top of the trajectory and how long does it take to get there?

b. (5 points) When the missile reaches the top of its trajectory, it fires thrusters that boosts its horizontal velocity to 5 km/sec. What is the total range of the missile?

Explanation / Answer

Here ,

initial speed , v = 4000 m/s

theta = 40 degree

a)

height at the top trajectory = ( v * sin(theta))^2/(2g)

height at the top trajectory = (4000 * sin(40))^2/(2 * 9.8)

height at the top trajectory = 3.37 *10^5 m

height at the top trajectory is 337.3 Km

time taken is t = v * sin(theta)/g

t = 4000 * sin(40)/9.8

t = 262.4 s

the time taken for the missile to get to top is 262.4 s

b)

when the total range

Range = v * cos(theta) * t + ( v * cos(theta) + 5000 ) * t

Range = ( 4000 * cos(40) + (4000 * cos(40) + 5000) ) * 262.4

Range = 2.92 *10^6 m

Range = 2920 km

the total range of missile is 2920 Km

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