Final answer:
The bullet fired at a 30-degree angle for 25 seconds has a velocity of projection of approximately 120 m/s, which can be calculated using the equations of motion for projectile motion.
Step-by-step explanation:
The question deals with the topic of projectile motion, in which a bullet is fired at an angle of 30 degrees to the horizontal. To find the velocity of the projection when the bullet stays in the air for 25 seconds, we utilize the equations of motion for projectile motion, considering a two-dimensional kinematic scenario.
Using the formula t = (2 * u * sin(θ)) / g, where t is the total time in air, u is the initial velocity, θ is the initial angle of projection, and g is the acceleration due to gravity (approx. 9.81 m/s²), we can solve for u. Given t is 25 seconds and θ is 30 degrees, we can rearrange the formula to u = (t * g) / (2 * sin(θ)).
Substituting the known values: u = (25 * 9.81) / (2 * sin(30°)). Solving this, we get the initial velocity u to be 122.625 m/s, which we can approximate to 120 m/s to match the given options. Thus, the correct answer is option (d) 120 m/s.