Final answer:
To hit an object 180 meters away with a muzzle speed of 80 meters per second, the angle of elevation should be approximately 15 degrees.
Step-by-step explanation:
To hit an object 180 meters away with a muzzle speed of 80 meters per second, we need to determine the angle of elevation. We can use the projectile motion equations to solve for the angle. Since there is no air resistance, the horizontal component of velocity remains constant throughout the motion. We can use the equation v = d/t to find the time of flight, where v is the horizontal velocity, d is the horizontal distance, and t is the time of flight. t = d/v = 180/80 = 2.25 seconds. To determine the angle of elevation, we can use the equation tan(theta) = (v_y/v_x), where theta is the angle of elevation, v_y is the vertical component of velocity, and v_x is the horizontal component of velocity. We can find the vertical component of velocity using the equation v_y = g*t, where g is the acceleration due to gravity and t is the time of flight. Substituting the values, we get v_y = 9.8 * 2.25 = 22.05 m/s. Now, substituting the values in the equation tan(theta) = (v_y/v_x), we get tan(theta) = 22.05/80. Solving for theta, we get theta = arctan(22.05/80) = 15 degrees (approximately).