Vectors and Trajectories, help with problems

In summary, Wiley Coyote runs off a cliff at 25 m/s and if he is 1.0 km away from the tower, he has to save Lois in 3 seconds. For problem 38, the correct way to solve it is to only look at the y motion.
  • #1
wakejosh
102
0
just a few similar problems.

38- A ball is rolled off a table with an initial speed of 0.24 m/s. A stop watch measures the ball's trajectory time from the table to the floor to be 0.3 s. What is the height of the table? (neglect air resistance)
a. 0.11m b. 0.22m c. 0.33m d. 0.44m

I think its D
For this I used a kinematics equation i found here: http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L6b.html to get values for the horizontal and vertical motions, I came up with 0.369 m so my guess would be C. is this wrong? Actually, Now that I look at this its a little tricky, and I think I should only be concerned with the motion in the y direction. If so I calculate y = 1/2(9.8)(.3^2) and I come up with y= 0.44 . So it looks like it may be D ??



16- A bridge that was 5 m long has been washed out by the rain several days ago. How fast must a car be going to successfully jump the stream? Although the road is level on both sides of the bridge, the road on the far side is 2m lower than the road on this side.
a. 5 m/s b. 8 m/s c. 13 m/s d. 25 m/s

I think it's B
I did practically the same for this: 2 = 1/2(9.8)(t^2) then i put V= 5m/0.64s and came up with 7.8 m/s so i guess it is B?


32- Wiley Coyote has missed the elusive road runner once again. This time, he runs off the edge of the cliff at 25 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land?
a. 112 m b. 225 m c. 337 m d. 400 m

I think it's A
Again, very similar, I found the T the same way:

100m = 1/2 * 9.8 m/s * T^2 and solving for T i got 4.52 seconds. then i put this in:
25 m/s = X/4.52 s and ended up with 113 m so I am pretty sure it's A. am i right?



29- Superguy is flying at treetop level near Paris when he sees the Eiffel Tower elevator start to fall (the cable snapped). His X-ray vision tells him Lois LaTour is inside and needs help. If Superguy is 1.0 km away from the tower, and the elevator falls from a height of 240m, how long does Superguy have to save Lois, and what must be his average velocity? (Superguy needs only touch Lois before she hits the ground because he is magically immune to the laws of physics and anyone he touches can also instantly become immune.)
a 3 s, 333 m/s b. 5 s, 200 m/s c. 7 s, 143 m/s d. 9 s, 111 m/s



I think it's C. 7s, 143 m/s
same thing:
240 = 1/2(9.8)(t^2), and i get t= 6.99 s
then 1000m/6.99s I get 143 m/s



(my backpack was stolen so I don't have my book with me, and it really sucks :(
 
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  • #2
could anyone check these for me? I'm not positive I'm doing them right.
 
  • #3
work looks good and the numbers seem to work out.
 
  • #4
I added two more problems if anyone could double check those for me as well. also,,, I think my answer was wrong in the first problem in the post so I changed it and only concerned myself with motion in the Y or falling direction.
 
  • #5
im still not sure about the first one (38), i can't decide which way is the right way to do it.
 
  • #6
bump.

please a simple yes/no is all I am looking for. can someone please just double check my work and see if i did them right? also on the first problem I am a little unsure.
 
  • #7
the correct way for 38 is to look at only the y motion. so the second way you did it is correct.
 
  • #8
great.. so all the rest look good I am assuming?
 

FAQ: Vectors and Trajectories, help with problems

What is a vector and how is it different from a scalar?

A vector is a quantity that has both magnitude and direction. This means that in addition to its numerical value, it also has a specific direction in space. A scalar, on the other hand, only has magnitude and does not have a direction. An example of a vector is velocity, which includes both speed and direction, while an example of a scalar is temperature, which only has a numerical value.

How do you add or subtract vectors?

To add or subtract vectors, you can use the head-to-tail method. Place the two vectors head-to-tail, meaning that the tail of one vector is placed at the head of the other. The sum or difference of the two vectors is then the vector that starts at the tail of the first vector and ends at the head of the second vector. This method can also be extended to more than two vectors by repeating the process.

What is a trajectory and how is it related to vectors?

A trajectory is the path that an object follows through space. It can be represented as a vector since it has both magnitude (the distance traveled) and direction (the direction in which the object is moving). This vector is known as the displacement vector and can be used to calculate the object's trajectory.

How do you calculate the angle between two vectors?

The angle between two vectors, A and B, can be calculated using the dot product formula: A · B = |A| * |B| * cos(θ). In this formula, |A| and |B| represent the magnitudes of the two vectors, and θ is the angle between them. By solving for θ, you can find the angle between the two vectors.

How are vectors and trajectories used in real-life applications?

Vectors and trajectories have many real-life applications, including navigation systems, flight paths, and sports analysis. They are also used in physics and engineering to study motion and forces. For example, in a car crash, vectors and trajectories can be used to analyze the direction and force of impact. In sports, vectors can be used to analyze the path of a ball or the trajectory of a player's movement.

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