Golf ball distance when hit down 45 degree slope

[dar|{anGel_]

umm... I'm not really used to using forums.. but whoever is online now and reading this... i would reaLLY appreciate if you could help me on this question.. this is fairly uRGent because its a bonus question which i want to hand in early tomorrow.

i've already spent a lot of time on it.. and i think i have the answer, but I'm still not sure of my answer.. Please help or attempt to help me by tonight..

Okay, here is the question:

A golfer is standing at the top of a hill that slopes downward at a 45 degree angle. If he hits his golf ball with an initial velocity of 30.0m/s forward, what distance (d) down the slope from him does the ball first strike the hill?

(sorry i can't draw the diagram here but if you don't understand the question i'll try to add a pic or sketch)

thanks..!

 

[dar|{anGel_]

oh yes.. the answer i got was 259.75 metres... is that correct?

 

[dar|{anGel_]

Full solution

i'll show my work here.. although i must admit it's hard to do all these formulas on the computer..

SOLUTION (i know this format is weird, but my physics teacher wants it in this format.. ps, i am doing this in components and i am not taking into consideration significant figures)

Let "up" and "forward" be positive, and "time zero" be the instant the golf ball is hit. (also let A repressent acceleration, V be velocity, T be time, x be the x-components and y be the y-components)

Horizontal Motion:
Xo = 0 m
Vox = 30.0 m/s
Ax = O m/s2

X = Xo + VoxT - 1/2 AxT2
X = 30.0T

Vertical Motion:
Yo = 0 m
Voy = 30.0 m/s
Ay = -9.8 m/s2

Y = Yo + VoyT - 1/2 AyT2
Y = -4.9t2

Since the hill is sloping downwards at an angle of 45 degrees, the X and Y component should be perpendicular, and the other angle should be 45 degree as well.

Thus the X and Y components can be equated (is this right?):
30.0T = -4.9T2
T = 6.122s (must be positive)

Therefore sub back into equation:
X = 30.0T
X = 183.67 m

Y = -4.9T2
Y = -183.67 m

Therefore to find distance (d) of the hill, use pythagorean theorum:
d2 = X2 + Y2
d2 = (183.67)2 + (-183.67)
d = 259.75 m

*sigh* that was long.. blah.. can anyone tell me if that was right please? thanks )

 

[dar|{anGel_]

isnt there anyone online?

 

[russ_watters]

Yep, you got the right answer - and just as a rule of thumb, even at night (when a lot of people are on) it usually takes an hour or two for a response.

And its probably just a typo (you didn't use it): Voy=0.

 

[HallsofIvy]

I agree with Russ_Watters although I would not necessarily have interpreted "initial velocity of 30.0m/s forward" to mean exactly horizontal. Of course, given the information, that's the only interpretation you can make- but I would have worried about it!

By the way, dar|{anGel_, please don't expect people to answer your questions instantly!

 

[dar|{anGel_]

THanks! )

um.. heh.. heh.. heh.. well, as i said, i wAS new to the forum and i was desperate to get the answer because i was about to give up on it since i worked on it for so long, and it wasnt until i realized that the angle being 45 degrees meant that the X and Y would be equal that i figured it out...

(i was doing to question according to a diagram given along with the question, which was reaLLY misleading, because it made the 45 degree angle really small, and therefore the X looked longer than the Y)

.. of course later, i realized it was so easy.. coz all you had to do was equate the two equations to get the time... i mean, the method was easier than i thought it would be because i assumed that it would require a lot more work (since it was a 'bonus' question given to my Gr. 12 Physics class, and i expected something reaLLY hard.. i guess if the angle was not 45 degrees it would be a lot harder.. but not impossible)



well.. i diDnt expect "instantly".. just within.. like.. minutes.. since you guys are soOOOooo presumably smart (was it wrong to overestimate your abilities?)

oh yes, and that was a typo.. the Voy was supposed to be zero.. (i copied and pasted it.. and forgot to change it)


Anywayss... Thanks a lot, russ_watters and HallsofIvy! i am completely and utterly humbled by your presence and superfluous amounts of knowledge in Physics (in other words, i'll just assume you guys are hard core Physics junkies with either too much time on your hands or are just really, really nice )

if you noticed, I am not exactly a Physics type person, but i like to blab on about nothing a lot (anyways, it looks like i'll become a permanent resident of your forum..i'll probably need it for the rest of my Physics-engrossed year)