CT2D- a Projectile Is Fired at an Angle Angle Q (Above the Horizontal) with Initial Speed V0

CT2D-1 A projectile is fired at an angle angle  (above the horizontal) with initial speed v0.

v 0 

What is the x-component of the initial velocity vector?

A) v0 cos B) v0 sin C) Neither of these

Answer: v0 cos

CT2D-2 The acceleration vector for an object is shown. From the graph, what can you say about the x- and y-components of the acceleration vector?

A) ax is negative; ay is positive.

B) ax is positive; ay is negative.

C) ax is positive; ay is positive.

D) ax is negative; ay is negative. E) None of these

Answer: None of these. The x-component of the vector is zero. Page 3 of 11

CT2D-3 A projectile is fired at an angle  with initial speed v0 from a table a height h above the floor. The projectile strikes the floor with a final speed v given by the formula 2 2 v= vx + v y .

v 0 

What is the correct formula for vx? A) v0cos B) v0sin C) Neither of these

Answer: v0 cosvx is constant in time. CT2D-4 A bullet is fired horizontally from a rifle on the Moon (where there is no air). The initial speed of the bullet when it leaves the gun barrel is vo. Assume that the ground is perfectly level (and endless). Page 4 of 11

I ) During its entire flight, the minimum speed of the bullet is vo. II ) The acceleration of the bullet is constant during its flight.

III ) The time it takes for the bullet to hit the ground increases as vo is increased. A ) All of the above statements are true. B) Only two of these statements is true. C) Only one of these statements is true.

Answer: B. Statement III is false. The others are true. As the bullet falls, its speed is given by

2 2 A) v0 B) vo + g t C) v0 + ( g t) D) vo – g t

2 2 Answer: v0 + ( g t) Page 5 of 11

CT2D-5 Two projectiles are fired from a cannon. For projectile A, the cannon is tilted upward at an angle twice that of projectile B. Both projectiles are fired with the same initial speed. (As usual, neglect air resistance.)

Which projectile was in the air longer? A) A B) B C ) A and B were in the air the same length of time. D ) Not enough information to answer the question.

Answer: A. Look at the y-motion only to determine which is in flight longer. Page 6 of 11

CT2D-6 A hunter shoots a monkey in intergalactic space (where there is no gravity). The bullet flies in a straight line and hits the monkey. The path of the bullet is described by the vector equation v v v r= ro + v o t y

Path of bullet finish

x When the time t is such that the bullet is half-way to the monkey, the vector rv is which vector on the diagram? D) None of these y

Answer: C. A is the vector r0. B is the vector v0t. Page 7 of 11

CT2D-7 A pellet is fired from a slingshot with initial speed vo at an angle . The projectile lands on a building. Where is the speed of the projectile a minimum? B

C v o A 

A) Immediately after the pellet is launched. B) At the apex of the trajectory. C) Just before the pellet hits the building. D) None of these, the speed is constant

Answer: At the apex.

CT2D-8 A rifle is accurately aimed at a rabid monkey hanging from the branch of a tree. The instant the gun is fired, the monkey releases the branch and starts falling. The monkey is well within the range of the rifle. The initial speed of the bullet is vo. What happens?

vo gun Page 8 of 11

A ) The bullet finds its target, regardless of the value of vo. (Assuming vo still large enough to reach the air below the monkey.)

B ) The bullet hits the monkey only if vo is large enough. C ) The bullet misses.

Answer: A. See the discussion in the lecture notes.

CT2D-9 Consider the velocities at times t1 and t2. These are the velocity vectors V1 and V2.

Draw the V1 + V = V2 vector diagram. What is the direction of V, the change in velocity between t1 and t2? A) straight up  B) straight down  C) upper right D) lower right

t t 2 1

v o 

Answer: straight down . The direction of V is the same as the direction of the acceleration a.

CT2D-10 True or False: If the speed of an object is constant, its acceleration must be zero. A) True B) False Page 9 of 11

Answer: False. An object moving with constant speed around a circle has a non-zero acceleration, because the direction of the velocity is changing. Page 10 of 11

CT2D-11 A particle is moving along the path shown, with constant speed. Its velocity vector at two different times is shown. What is the direction of the acceleration when the particle is at point X?

D (E) None of these

Answer: A. Draw the V1-V2-deltaV diagram!

CT2D-12 A race car travels around the track shown at constant speed. Over which portion of the track is the magnitude of the acceleration the smallest? 2 4

A) From 1 to 2 B) From 3 to 4 C) Neither of these D) Both of these Page 11 of 11

Hint: it’s a trick question !

Answer: Neither of these. The acceleration is zero on the straight portions of the track.