Final answer:
The problem requires using equations of motion to find both the time to reach the highest point of projectile motion and the horizontal distance traveled. By decomposing the initial velocity into vertical and horizontal components and applying kinematic equations, the correct option can be determined.
Step-by-step explanation:
The question involves calculating the time taken for a projectile to reach its highest point and the horizontal distance traveled. To start with, we decompose the initial velocity of the projectile into its vertical and horizontal components. The time to reach the highest point can be found using the vertical component and the equation v = u + at, where v is the final velocity (which is 0 m/s at the highest point), u is the initial vertical velocity, and a is the acceleration due to gravity (which is -9.8 m/s2 since it acts downwards).
The initial vertical velocity (uy) is calculated as uy = u * sin(θ) where u is the initial velocity and θ is the launch angle. Substituting the values, uy = 301 m/s * sin(3°). The time taken to reach the highest point (t) is given by t = uy / g. Once the time is calculated, the horizontal distance (x) is found using the horizontal component of velocity (ux) and the time: x = ux * t, where ux = u * cos(θ).
Using the above steps, we can eliminate option (A) and (B) as they do not account correctly for the effect of gravity or the angle of launch on the horizontal distance. Options (C) and (D) are evaluated by performing the calculations, one of which provides the matching answer.