Re: Physics... math problem

novelo wrote: 
Hello. I've got the following problem but I do not know if it
solvable... I've been trying os far many methods, but still I cannot
get it.

Check is out:

In a golf camp a hole is at 240ft horizonatlly and 64ft vertically. The
ball hits the hole 4 seconds after it was hit.
Get the magnitude and direction of the ball... Hence, get the Vo and
the angle.


I would assume (based on the type of problem) that the ball is assumed
to fly directly to the hole from the tee, under constant acceleration
due to gravity. This is a standard type of problem when studying
motion under constant acceleration.

Since acceleration due to gravity is in the vertical (downward)
direction, the velocity in the horizontal (x-) direction is constant.
You know delta x to be 240 feet, and you know that delta t is 4 sec,
so you can compute v_x, the horizontal component of velocity:

	v_x = delta x / delta t = 240/4 = 60 ft/sec

Next, you know (or should assume) that the ball travels upwards from
the shot, reaches some maximum height, and comes downward to hit the
hole, and you know that the acceleration is constant, a_y = -g (g being
the absolute value of acceleration due to gravity: g = 9.8 m/s^2 ~ 32 ft/s^2). You know that the vertical displacement in 4 seconds is 64 feet, so you can use y = v_y t - g t^2/2 to solve for the initial
y-component of velocity, v_y:

	64 = v_y * 4 - 32 * 4^2/2

so

	4 v_y = 64 + 32*4^2 / 2

	4 v_y = 64 + 32*8 = 64 + 256

	4 v_y = 320, so v_y = 80 ft/sec.

Put it all together, and you have initial velocity v = <v_x, v_y>

	v = <60 ft/sec, 80 ft/sec>

this gives a speed of 100 ft/sec, at an angle equal to
inverse tangent of 4/3, approximately 53.1 degrees above
horizontal.

Dale.




+ We cannot divide the time between 2 to know the maximun height
because the altitude where you hit the ball is cero and the altitude of
the hole is 64ft.
+ We cannot divide the distance in X either to get the highest point.

Hence we cannot get the Vo of y neverthelles for X, Vo=64ft/s

I've though to make this a parabola in the analytical geometry way...
But we cannot get any info because the vertex, is unknown... (x,y) and
therefore we cannot know the x-intercepts.

I've tryed to do a relation, but I don't know if it will work...

Since x=240 when y=64, when when y=0, x is?
But the answer will be zero! And that cannot be that way! X keeps on
growing forever while x is positive in a part and negative in the
other...

So... I think this problem is impossible to solve.
If anyone has the answer or a key to get to it, that will be very
helpfull.
Maybe you think I am a little naive with this stupid high school
problems, :P But it's kinda hard for me since I'm only about to enter
high school and I've never seen this themes. I'm studying with books,
so any help from you will really help me get more knowledge. Thank you
once again!

.

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