Conceptual Physics Free fall and Projectile Motion Test

Angled Projectiles Steps

1. Solve for x and y components (vix/viy) using trig: Launch velocity(cos(launch angle))= vix Launch velocity(sin(launch angle))= viy 2.Solve for time up using equation: vfy=viy+(ay)(t) 3. Multiply time by 2 to get full/total time 4. Use equation : x=(vix)(t)+1/2(a)(t^2) to get horizontal (x) displacement Use TOTAL time 5. Use equation: y=(viy)(t)+1/2(a)(t^2) to get height/ y at peak Use HALF time/ time up

Horizontal Projectiles Steps

1. Establish givens (ax=0m/s^2) (ay=-9.8m/s^2 or -10m/s^2). (viy=0m/s) 2. Use equation: x=(vix)(t)+1/2(a)(t^2) y=(viy)(t)+1/2(a)(t^2) to solve for remaining variables

37. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, the net force acting upon it is _______. (Neglect the effects of air resistance.) a. entirely vertical b. entirely horizontal c. both vertical and horizontal d. not enough information given to know.

Answer: A A projectile is an object upon which the only force is gravity. Since no other forces act upon the object, the net force would be downward.

36. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, its acceleration is _______. (Neglect the effects of air resistance.) a. entirely vertical b. entirely horizontal c. both vertical and horizontal d. not enough information given to know.

Answer: A As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. This is to say that the acceleration of the object is vertical, not horizontal. At the peak and everywhere throughout the trajectory, there is a vertical (downward) acceleration. In fact, a projectile is an object upon which the only force is gravity. This force causes an acceleration which is in the same direction as the force - downward.

34. An object is undergoing free fall motion. As it falls, the object's ____. a. speed increases b. acceleration increases c. both of these d. none of these

Answer: A As an object free-falls, its velocity (and also its speed) changes by approximately 10 m/s every second. This means that the acceleration is a constant value of 10 m/s/s. An object has a changing speed (or velocity) and a constant acceleration if the speed changes by the same amount (a "constant amount") in each consecutive second of its motion.

45. Two projectiles are fired at equal speeds but different angles. One is fired at angle of 30 degrees and the other at 60 degrees. The projectile to hit the ground first will be the one fired at (neglect air resistance) ____. a. 30 degrees b. 60 degrees c. both hit at the same time

Answer: A For projectiles launched at angles, a launch angle of 45 degrees will provide the largest horizontal displacement. Launch angles greater than 45 degrees result in large vertical components of velocity; these stay in the air longer and rise to higher heights. Launch angles less than 45 degrees result in small vertical components of velocity; these do not rise as high and end up falling to the ground in shorter times.

6. Which of the following statements are true of projectiles? List all that apply. a. A projectile is a free-falling object. b. A projectile experiences negligible or no air resistance. c. A projectile must be moving in the downward direction. d. A projectile must be accelerating in the downward direction. e. A projectile does not have to have horizontal motion. f. A projectile could begin its projectile motion with a downward velocity. g. A projectile does not need to be "falling."

Answer: ABDEF and possibly G

35. A football is kicked into the air at an angle of 45 degrees with the horizontal. At the very top of the ball's path, its velocity is _______. a. entirely vertical b. entirely horizontal c. both vertical and horizontal d. not enough information given to know.

Answer: B As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. At its peak, its vertical velocity becomes 0 m/s. At this instant in time, the velocity is entirely horizontal; there is no vertical component to the velocity.

42. Roll a bowling ball off the edge of a table. As it falls, its horizontal component of velocity ___. a. decreases b. remains constant c. increases

Answer: B Once the ball leaves the table's edge, it becomes a projectile. As it falls, its horizontal velocity remains constant while its vertical velocity decreases. This is to say that the acceleration of the object is vertical, not horizontal. In fact, a projectile is an object upon which the only force is gravity. This force causes an acceleration which is in the same direction as the force - downward.

9. Which of the following statements are true of the time of flight for a projectile? List all that apply. a. The time that a projectile is in the air is dependent upon the horizontal component of the initial velocity. b. The time that a projectile is in the air is dependent upon the vertical component of the initial velocity. c. For a projectile which lands at the same height that it is projected from, the time to rise to the peak is equal to the time to fall from its peak to the original height. d. For the same upward launch angles, projectiles will stay in the air longer if the initial velocity is increased. e. Assume that a kicked ball in football is a projectile. If the ball takes 3 seconds to rise to the peak of its trajectory, then it will take 6 seconds to fall from the peak of its trajectory to the ground.

Answer: BCD

39. At what point in its path is the vertical component of the velocity (vy) of a projectile the smallest? a. The instant it is thrown. b. Halfway to the top. c. At the top. d. As it nears the top. e. It is the same throughout the path.

Answer: C As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. During the upward portion of its trajectory, the vycontinuously decreases until it becomes 0 m/s at the peak. Thus, the vy is as small as it will ever be when it is at the peak of the trajectory.

43. A bullet is fired horizontally and hits the ground in 0.5 seconds. If it had been fired with twice the speed in the same direction, it would have hit the ground in ____. (Assume no air resistance.) a. less than 0.5 s. b. more than 0.5 s. c. 0.5 s.

Answer: C Once the bullet leaves the muzzle, it becomes a projectile (assuming no air resistance). As it falls, its horizontal velocity remains constant while its vertical velocity decreases. The force of gravity acts upon the bullet to cause its downward acceleration. The motion of the bullet in the downward direction is independent of the motion in the horizontal direction. That is to say, any alteration in a horizontal aspect of its motion will not effect the motion in the vertical direction. The time to fall vertically to the ground is not effected by the horizontal speed of the projectile. It would still take 0.5 seconds to fall to the ground from this height regardless of the horizontal speed.

8. Which of the following statements are true of the vertical motion of projectiles? List all that apply. a. The vertical component of a projectile's velocity is a constant value of 9.8 m/s. b. The vertical component of a projectile's velocity is constant. c. The vertical component of a projectile's velocity is changing. d. The vertical component of a projectile's velocity is changing at a constant rate. e. A projectile with an upward component of motion will have a upward component of acceleration. f. A projectile with an downward component of motion will have a downward component of acceleration. g. The magnitude of the vertical velocity of a projectile changes by 9.8 m/s each second. h. The vertical velocity of a projectile is 0 m/s at the peak of its trajectory. i. The vertical velocity of a projectile is unaffected by the horizontal velocity; these two components of motion are independent of each other. j. The final vertical velocity of a projectile is always equal to the initial vertical velocity. k. The vertical acceleration of a projectile is 0 m/s/s when it is at the peak of its trajectory. l. As a projectile rises towards the peak of its trajectory, the vertical acceleration will decrease; as it falls from the peak of its trajectory, its vertical acceleration will decrease. m. As a projectile rises towards the peak of its trajectory, the vertical acceleration is directed upward; as it falls from the peak of its trajectory, its vertical acceleration is directed downward. n. The peak height to which a projectile rises above the launch location is dependent upon the initial vertical velocity. o. As a projectile rises towards the peak of its trajectory, the vertical velocity will decrease; as it falls from the peak of its trajectory, its vertical velocity will decrease. p. Consider a projectile launched from ground level at a fixed launch speed and a variable angle and landing at ground level. The vertical displacement of the projectile during the first half of its trajectory (i.e., the peak height) will always increase as the angle of launch is increased from 0 degrees to 90 degrees. q. Consider a projectile launched from ground level at a fixed launch angle and a variable launch speed and landing at ground level. The vertical displacement of the projectile during the first half of its trajectory (i.e., the peak height) will always increase as the launch speed is increased.

Answer: CDFGHINPQ

44. A projectile is launched at an angle of 15 degrees above the horizontal and lands down range. For the same speed, what other projection angle would produce the same downrange distance? a. 30 degrees. b. 45 degrees. c. 50 degrees. d. 75 degrees e. 90 degrees.

Answer: D For projectiles launched at angles, a launch angle of 45 degrees will provide the largest horizontal displacement. Any two launch angles which are separated from 45 degrees by the same amount (for example, 40 degrees and 50 degrees, 30 degrees and 60 degrees and 15 degrees and 75 degrees) will provide the same horizontal displacement.

5. Which of the following descriptions of moving objects accurately portray a projectile? List all that apply. a. an object which is moving through the air and not touching any surface b. a falling skydiver with an open parachute c. any object upon which air resistance is negligible d. a free-falling object e. an object upon which the only significant force is the force of gravity f. a falling feather g. a falling feather in a vacuum chamber h. a falling feather in a falling vacuum chamber.

Answer: DEGH A projectile is an object upon which the only force is gravity. Air resistance must be negligible or nonexistent. Other forces resulting from people or things pulling or pushing, attached strings or contact with surfaces must not be present.

7. Which of the following statements are true of the horizontal motion of projectiles? List all that apply. a. A projectile does not have a horizontal velocity. b. A projectile with a rightward component of motion will have a rightward component of acceleration. c. The horizontal velocity of a projectile changes by 9.8 m/s each second. d. A projectile with a horizontal component of motion will have a constant horizontal velocity. e. The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory. f. The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other. g. The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity. h. The final horizontal velocity of a projectile is always equal to the initial horizontal velocity. i. As a projectile rises towards the peak of its trajectory, the horizontal velocity will decrease; as it falls from the peak of its trajectory, its horizontal velocity will decrease. j. Consider a projectile launched from ground level at a fixed launch speed and a variable angle and landing at ground level. The horizontal displacement (i.e., the range) of the projectile will always increase as the angle of launch is increased from 0 degrees to 90 degrees. k. Consider a projectile launched from ground level at a fixed launch angle and a variable launch speed and landing at ground level. The horizontal displacement (i.e., the range) of the projectile will always increase as the launch speed is increased.

Answer: DFGHK

38. At what point in its path is the horizontal component of the velocity (vx) of a projectile the smallest? a. The instant it is thrown. b. Halfway to the top. c. At the top. d. As it nears the top. e. It is the same throughout the path.

Answer: E As a projectile rises towards its peak, its horizontal velocity remains constant while its vertical velocity decreases. This is to say that the acceleration of the object is vertical, not horizontal. Having a constant horizontal velocity, there is no point along the trajectory where the vx value is smaller than at other points.