2. Sketch a V(T) Graph That Would Be Associated with the A(T) Graph Shown Below

PHY 113, Summer 2007

Langenbrunner

HW 2 – due Wednesday, May 30

1. On the drive from Cincinnati to Rochester, I am traveling at 60 mph, 3 seconds behind a big truck in front of me (that is, the front of my car passes the same point in the road 3 seconds after the truck clears it). The trucker suddenly spots a dead deer in the road, and he swerves just in time. Unfortunately, I am "boxed in" and cannot swerve without hitting another car, so my only chance is to slam on my brakes. Can I stop in time? (Assume a truck length of 20 m, a reaction time of 400 ms, and an average deceleration of 5.18 m/s2.)

2. Sketch a v(t) graph that would be associated with the a(t) graph shown below.

(First, redraw the curve below, taking care to label axes. You are encouraged to draw both a(t) and v(t) curves on the same graph – but if you do, make sure you label each curve separately.)

3. An enraged Rachael drops Ross' belongings one by one out of their apartment window (15 m high). One second after she drops a open box of random items (books and rocks on the bottom, soft cottony sheets on the top), she spots Ross himself, standing open-mouthed, on the ground below, and she angrily throws the next item – a very delicate and important dinosaur bone – straight down. Much to her dismay and much to his delight, the bone softly lands right in the box just as the box hits the ground, preventing paleontological disaster.

a) How long was Ross' shriek? (Assume he shrieked for the entire length of the bone's fall.)

b) What initial speed did Rachael impart on the dino bone?

c) How fast was the bone moving right before it landed in the box?

d) Now redo the problem and switch your choice of positive direction (but keep your choice of origin). Make sure the answers are consistent.

4. (This problem is optional. It's good, but long. Do it for extra practice if you'd like.) As the picture below shows, Clara jumped from a bridge, followed closely by Jim. How long did Jim wait after Clara jumped? Assume that Jim is 170 cm tall and that the jumping-off level is at the top of the figure.

5. Can the sum of the magnitudes of two vectors ever be equal to the magnitude of the sum of the same two vectors? If no, why not? If yes, when?

6. An ant, crazed by the Sun on a hot Texas afternoon, darts over an xy plane scratched in the dirt. The x and y components of four consecutive darts are the following, all in centimeters: (30.0, 40,0), (bx, -70.0), (-20.0, cy), (-80.0, -70.0). The overall displacement of the four darts has thexy components (-140, -20.0). What are

a) component bx,

b) component cy,

c) the magnitude, and

d) the direction of the overall displacement?

7. A frightened rabbit runs onto a large area of level ice that offers no resistance to sliding, with an initial velocity of 6.0 m/s toward the east. As the rabbit slides across the ice, the force of the wind causes it to have a constant acceleration of 1.4 m/s2, directed due north. Choose a coordinate system with the origin at the rabbit's initial position on the ice and the positive x axis directed toward the east. After the rabbit's has slid for 3.0 s, what (in unit-vector notation) are its

a) velocity, and

b) position?

8. A European starling, with a worm in its beak, travels horizontally at a speed of 5 m/s, 10 m above the ground. I am sitting on top of a rock on the ground such that my head is 1 m above the ground. If the bird accidentally drops the worm when it is 6.5 m away from me in the x-direction (still approaching, as the picture indicates), will the worm land on my head? If not, how far away from me will it land (when it lands on the ground, that is)?

9. About 4000 car-train collisions occur in the United States each year. Many occur when a driver spots an oncoming train and then attempts to beat it to a railroad crossing. Consider the following situation: One of those 4000 drivers spots a train on a track that is perpendicular to the roadway and judges the train's speed to be equal to his speed of 30.0 m/s. The train and the car are both approaching the rail crossing, as shown below. The driver figures that by accelerating his car at a constant 1.50 m/s2 toward the crossing, he should reach it first. The distance between the car and the center of the crossing are both equal to 40.0 m. The length of the car is 5.0 m, and the width of the train is 3.00 m.

a) Is there a collision?

b) If not, by how much time does the driver miss a collision; if so, how much more time is needed to barely miss the collision?

c) On a position vs. time graph, plot the location of the train and the location of the car (label the axes and each separate curve) as a function of time.

10. A policeman chases a master jewel thief across city rooftops. They are both running at 5 m/s when they come to a gap between buildings that is 4 m wide and has a drop of 3m. The thief, having studied a little physics, leaves at 5 m/s at 45° from the horizontal and clears the gap easily. The policeman did not study physics and thinks he should maximize his horizontal velocity, so he leaves at 5 m/s horizontally.

a) Does the policeman clear the gap?

b) By how much does the thief clear the gap?

11. A gibbon hangs from a tree branch, as shown. A distance away, a poacher, quite familiar with the ways of gibbons and partially familiar with the laws of physics, aims his hunting rifle toward a point 2 m below the gibbon. You see, he knows that as soon as he shoots, the gibbon, startled by the noise, will drop from the tree. The poacher has calculated, furthermore, that during the time it takes his bullet to get to the gibbon, the gibbon will have fallen 2 m. How clever. The poacher checks his notes, lines up the shot, and pulls the trigger. The gibbon drops, but lands on the ground, unharmed, and scampers off into the jungle.

a) What did the poacher forget from his physics class?

b) How far below the falling gibbon did the bullet pass?