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.
- 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.
- What is the initial horizontal velocity, vxi, in m/s? (Hint: The correct answer is between 0 and 40.)
- What is the initial vertical velocity, vyi, in m/s? (Hint: The correct answer is between 0 and 40.)
- What is the horizontal acceleration, ax, in m/s2? (Hint: The correct answer is between 0 and 40.)
- What is the vertical acceleration, ay, in m/s2? (Hint: The correct answer is between -40 and 40.)
- What is the final horizontal velocity, vxf, in m/s? (Hint: The correct answer is between 0 and 40.)
- (2A) How long is the ball in the air? (Hint: The correct answer is between 0 and 10.
- (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.
- 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?
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.
- (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.)
- 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?
- (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.)
- (4C) How long (in hours) does this satellite take to orbit Earth? (Hint: The correct answer is between 2 and 48.)