Question

An M-16 is fired from level ground at an upwards angle of 10 degrees with respect to the horizontal. The initial velocity of the bullet is 948 m/s, but because it is fired at a 10 degree angle, the vertical component of the initial velocity is 165 m/s and the horizontal component is 934 m/s. Ignore air resistance and the curvature of the earth in this problem. (Hint: See the videos Projectile Motion Parts 9-13. For questions 9-14 and 17, you do not need to do any calculations; these questions can be solved from information given in the problem and with concepts from the lecture videos.) What is the initial horizontal velocity, vxi, in m/s? (Hint: The correct answer is between 0 and 1000.) What is the initial vertical velocity, vyi, in m/s? (Hint: The correct answer is between 0 and 1000.) What is the horizontal acceleration, ax, in m/s2? (Hint: The correct answer is between 0 and 1000.) What is the vertical acceleration, ay, in m/s2? (Hint: The correct answer is between -500 and 500.) What is the final horizontal velocity, vxf, in m/s? (Hint: The correct answer is between 0 and 1000.) What is the final vertical velocity, vyf, in m/s? (Hint: The correct answer is between -500 and 500.) (3A) At the peak of its flight, what is the velocity (in m/s) of the bullet in the horizontal (x) direction? (Hint: The correct answer is between 0 and 1000.) (3B) At the peak of its flight, what is the velocity (in m/s) of the bullet in the vertical (y) direction? (Hint: The correct answer is between 0 and 1000.) What is the height difference, Δy, (in m) between the point where the bullet is fired and the point where the bullet lands? (Hint: The correct answer is between 0 and 100.) (3C) How long is the bullet in the air? (Hint: The correct answer is between 5 and 50. Find the full time of flight.) (3D) How far (in m) does the bullet travel horizontally? (Hint: The correct answer is between 10,000 and 40,000. Use the value for the time of flight found in part C in the appropriate kinematic equation for the horizontal x-direction to find the distance traveled.) If air resistance were considered, how would this affect the horizontal distance the bullet traveled? (3E) At what other angle (in degrees) could the gun be fired and travel the same horizontal distance? (Hint: See the videos in Lecture/Lesson on Projectile Motion/ Launch angles and Range. There is a symmetry in distances traveled by projectiles about the angle 45 degrees; therefore, projectiles fired at complementary angles will travel the same distance. See slide 11 in the Powerpoint.)

Answer 1