Kinematics: Solving Problems in Motion

[tnhoots]

kinematics PLEASE HELP!

I am having trouble with three questions on a homework set. Could someone please offer help as how to solve these problems. Other examples would be great! I'm not asking for someone to solve the probs. Just lead me in the right direction. This is my first physics course. And I am completely lost. Any help would be appreciated. I don't even know where to begin. Thanks

1) A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 15.0 m/s, and the distance from the limb to the level of the saddle is 3.00 m.

(a) What must be the horizontal distance between the saddle and limb when the ranch hand makes his move? (answer in meters)

(b) How long is he in the air? (answer in seconds)


2)The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration -5.05 m/s2 for 4.40 s, making straight skid marks 60.8 m long ending at the tree. With what speed does the car then strike the tree?
(answer in m/s)


3) A particle moves along the x axis. Its position is given by the equation x = 1.60 + 2.50t - 3.50t2 with x in meters and t in seconds.
(a) Determine its position when it changes direction. (answer in meters)
(b) What is its velocity when it returns to the position it had at t = 0?
(answer in m/s)

 

[berkeman]

Welcome to the PF, tnhoots. An important rule here is that you must show your own work in order for us to help you. It is also a good idea for you to use the Homework Posting Template that came up when you started this thread. If you had, you would have had to fill in the relevant equations that apply to these problems, and show us your attempt at a solution.

So let's start there. What are the relevant equations for these problems? How would you go about using them to solve the first question?

 

[Gregie666]

as for the first question:
calculate how long its going to take the rancher to drop from the level of the branch to the level of the horse (remember that he's falling at a constant accleration of g).
then calculate how far the horse will gallop during that time. let's call that distance X.

the rancher will want to drop from the branch when the horse still has X meters to cover before it reaches the branch...

 

[weatherhead]

1) ok the simplest way to try and tackle this one is to work out part b) first. Use the kinematic equations of motion (I am assuming you're allowed to assume no air resistance, everything can be modeled as a particle, etc.). Work out the time it takes the guy to fall from the tree to the horse's level. Now, bear in mind, as with simple projectile motion questions, the one thing that is the same between the horizontal and vertical velocity components is the time. Does that help?

2) another kinematic equations of motion question. However, you don't often see a question where they don't give you the the initial velocity of the car. Hint: try s=ut+0.5at^2 to solve for u, then use v=u+at to find v. If you're feeling adventurous, you can derive an equation to find v in one shot from these two, but if you prefer messy numerical calculations then crack on.

3)Treat this as a graph problem. Imagine drawing a graph of the function, and think about what it means when it "changes direction". There are two ways to find out what you're looking for. If you know calculus that's the obvious way, and if you go this route then you should find part b easy (as long as you realize that "velocity" is the time derivative of position.) On the other hand, if you don't do calculus yet, which when I was given those type of problems in physics I didn't, you'll need to complete the square for the first part. For part b, you'll then need to find a value for x first (tip: solve the equation), then use kinematic equations to find a corresponding value for v.

Hope that's enough hints for you.

 

[weatherhead]

oops, sorry. Don't try calculus on the third problem, far far simpler to just use some quadratic tinkering.