Applied Maths Help

Cian_

Posted this in leaving cert thread, but will probably get a better response here. Sorry for double post.

Just looking for a bit of help with an applied maths question.

A ball is kicked from a point P on level ground. It hits the ground for the first time 27m from P after 3 seconds. During it's flight, the ball just passed over a vertical wall standing 5.4m from P.
Find:
i) The horizontal and vertical components of the initial velocity of the ball
ii) the height of the wall
iii) the speed of the ball as it passed over the wall.

Yakuza

I won't do the problem for you, as it's against the ethos of this forum, but am happy to give you some pointers.

For these kinds of questions, we can assume that the velocity in the horizontal direction is constant (ignore friction due to air). As far as the vertical component goes, it starts off at whatever is imparted to it (from the gun, boot, golf club, whatever) and goes to zero as it reaches the top of its arc, then starts to increase again until it hits the ground.

In this problem, it is safe to assume that the arc the ball follows is symmetrical (if the object started on a raised platform or was travelling under an inclined plane, that would make things a little more complex (but not overly, once you have the principles down)).

Ok, getting back to this problem:

i-a) You're told the ball touches down 27m away (in a horizontal direction) in 3 seconds - can you work out its horizontal speed in m/s?
i-b) You can assume the only force acting on the ball in the vertical direction is gravity, and the ball reaches zero velocity in 1.5 seconds (the top of the arc,half way from P to where it hits the ground), so what is the initial speed? (hint: v = u+at, a will be negative as gravity as acting in the opposite direction to the ball's path (on the way up, at least))

ii) Now that you know the (constant) horizontal component, and a formula for the vertical component, what time would the ball take to reach 5.4m from P (using the horizontal speed)? Plug this time into the s = ut + [latex]\frac{1}{2}[/latex]at² equation to work out the height, where u is the inital vertical velocity worked out in i-b).

iii) To work out the speed of the ball, I presume the question wants you to work out the magnitude of the resultant vector (sorry, I forget some of the terms; it's over 25 years since I was studying applied maths!). You'll need to work out the vertical velocity of the ball (v=u+at again, at t=the time from part ii). Then just use Pythagoras and get the square root of the sum of the squares of the horizontal and vertical velocities.

Post back with how you get on.

EoghanIRL

Cian_ wrote: »

Posted this in leaving cert thread, but will probably get a better response here. Sorry for double post.

Just looking for a bit of help with an applied maths question.

A ball is kicked from a point P on level ground. It hits the ground for the first time 27m from P after 3 seconds. During it's flight, the ball just passed over a vertical wall standing 5.4m from P.
Find:
i) The horizontal and vertical components of the initial velocity of the ball
ii) the height of the wall
iii) the speed of the ball as it passed over the wall.

I've never seen an exam paper question like this before , is it from a text book .