Kinematics PLEASE HELP

as for the first question:
calculate how long its gonna 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. lets 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...

 

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 modelled 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 realise 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.

 

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