Reference no: EM131461572

At the instant a bullet (Bullet A) is being fired horizontally from a gun, an identical bullet (Bullet B) is dropped from the same height as the muzzle of the firing gun.

1. Briefly describe the order in which bullets A and B hit the ground.  (Hint: In both situations, what determines how long the bullet is in the air is the vertical motion. The horizontal motion does not affect how long the bullets are in the air. 

A softball coach throws a 1 kg ball horizontally to her player with an initial velocity of 40 m/s. The ball leaves her hand at 6 m high, and her catcher is 20 meters away. 

1. What is the initial horizontal velocity, v_xi, in m/s? (Hint: The correct answer is between 0 and 40.)
2. What is the initial vertical velocity, v_yi, in m/s? (Hint: The correct answer is between 0 and 40.)
3. What is the horizontal acceleration, a_x, in m/s²? (Hint: The correct answer is between 0 and 40.)
4. What is the vertical acceleration, a_y, in m/s²? (Hint: The correct answer is between -40 and 40.)
5. What is the final horizontal velocity, v_xf, in m/s? (Hint: The correct answer is between 0 and 40.)
6. (2A) How long is the ball in the air? (Hint: The correct answer is between 0 and 10. 
7. (2B) How many meters above the ground is the ball when it arrives at the catcher?  (Hint: The correct answer is between 0 and 10. Use the value for the time of flight found in part A in the appropriate kinematic equation for the vertical y-direction to solve for the height dropped in that time.)

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.  

1. What is the initial horizontal velocity, v_xi, in m/s? (Hint: The correct answer is between 0 and 1000.)
2. What is the initial vertical velocity, v_yi, in m/s? (Hint: The correct answer is between 0 and 1000.)
3. What is the horizontal acceleration, a_x, in m/s²? (Hint: The correct answer is between 0 and 1000.)
4. What is the vertical acceleration, a_y, in m/s²? (Hint: The correct answer is between -500 and 500.)
5. What is the final horizontal velocity, v_xf, in m/s? (Hint: The correct answer is between 0 and 1000.)
6. What is the final vertical velocity, v_yf, in m/s? (Hint: The correct answer is between -500 and 500.)
7. (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.)
8. (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.)
9. 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.)
10. (3C) How long is the bullet in the air?  (Hint: The correct answer is between 5 and 50. Find the full time of flight.)
11. (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.) 
12. If air resistance were considered, how would this affect the horizontal distance the bullet traveled.
13. (3E) At what other angle (in degrees) could the gun be fired and travel the same horizontal distance?  

The mass of Earth is 5.972 * 10²⁴ kg, and the radius of Earth is 6,371 km. A 750 kg satellite orbits 35,800 km above Earth in a perfectly circular orbit.  

1. (4A) What is the magnitude of the gravitational force (in Newtons) on the satellite due to Earth?  (Hint: The correct answer is between 100 and 200.)
2. If the gravitational force is the centripetal force keeping the satellite in a stable circular orbit, how does the centripetal force compare to the gravitational force?
3. (4B) If the gravitational force is the centripetal force keeping the satellite in a stable circular orbit, what is the tangential velocity (in m/s) of the satellite in its orbit? (Hint: The correct answer is between 10,000 and 40,000.)
4. (4C) How long (in hours) does this satellite take to orbit Earth?  (Hint: The correct answer is between 2 and 48.)