How Do You Solve the Freefall Catching Problem in Physics?

[chiamocha]

Freefall "catching" problem

Homework Statement

I have been having trouble understanding this physics problem and am so confused as to how I would even start.

Two friends are playing "catch" on a level playing field. At t=0 the are at x = 0. At t = 0, the catcher is run-in in the positive x direction, with constant speed v0. At a later time t, the thrower tosses the all from ground level, with the ball's horizontal motion the in +x direction. The initial peed of the ball is 4v0. The initial velocity of the ball makes an angle (theta) with the x axis. The catcher catches the ball at time tc, just as it reaches the ground.

Solve for the time tc when the ball reaches the ground. Express your answer in terms of v0, (theta) t1, g(as magnitude of acceleration due to gravity), and/or other constants.

Solve for time t1 at which the ball must be thrown in rode to be caught by the catcher.

I would really like help on how I would first begin these two problems, then hopefully I can figure it out from there but, I am not sure how I would use an equation to find a time when the ball reaches the ground, wouldn't that just be when t=0 again? And I don't know how I would go about finding how I would know when the catcher could catch the ball. Any starting help would be greatly appreciated.

 

[SteamKing]

In this problem, t is not a spatial parameter. t represents 'time', so if the ball is thrown at t = 0, then t is not going to equal 0 again, unless you invent a machine capable of going back in time.

This is a problem in projectile motion. You have done projectile motion problems before, I trust?

 

[chiamocha]

I have a formula sheet that has the formulas that are used for projectile motion. But this is really my first exposure to these type of problems which is why I am having so much trouble even understanding them just conceptually.

 

[SteamKing]

In general, you separate the vertical motion of the ball from its horizontal motion and analyze them separately. The vertical motion of the ball is affected by gravity, while the horizontal motion remains unaffected, unless resistance due to motion thru air is to be considered (which, in these problems, is apparently not).

You are given the initial speed of the ball and the angle at which it is thrown. Can you determine the horizontal and vertical components of the ball's velocity?