Final answer:
The value of the angle θ that a missile makes with the vertical when launched with a velocity of 250 m/s cannot be determined without additional information such as the maximum height or impact velocity. Projectile motion involves both vertical and horizontal components which would be used to solve for the angle.
Step-by-step explanation:
The question refers to a missile projected with a velocity of 250 m/s at an angle θ to the vertical, with a total flight time of 25 seconds. To determine the value of the angle θ, we would need to consider the projectile motion of the missile in both the vertical and horizontal components.
Since the question asks for the angle to the vertical, we need to find the vertical component of the initial velocity. However, without further information on the missile's motion, such as its maximum height reached or impact velocity, we cannot provide a definitive answer to the value of angle θ. Typically, one would use the formula for vertical motion in projectile motion, which is vy = v·sin(θ), where vy is the vertical component of the velocity and θ is the angle made with the horizontal. With the given information, it is not possible to calculate the angle. It's important to have complete information when solving such physics problems.