help on problem

kwinrow · 2008-07-31 09:08:28

7.) If an object is thrown on the moon, then the parametric equations of flight are:

x=(vcostheta)t and y=(vsintheta)t-2.66t^2+h.

Estimate the distance that a golf ball hit at 88 ft. per sec (60 mph) at an angle of 45 degrees with horizontal travels on the moon if the moon's surface is level.

how would i go about sloving this?where would i start?

mathsyperson · 2008-07-31 10:24:37

In those parametric equations, the variables mean these things:

x - horizontal distance from starting point
y - vertical distance from starting point
v - velocity of strike
theta - angle of strike
t - time since strike

(h would be used if the ground was uneven, but since it isn't you can ignore it)

Using the information given and plugging in what you know gives:

x = (88*cos45)t
y = (88*sin45)t - 2.66t²

When the ball lands, its vertical distance (y) will be 0.
So setting y = 0 in the second equation and solving will give you the time the ball spent in the air.
(It'll also give you 0, since the ball was on the ground as it was being hit)

Put your value of t into the first equation to tell you how much it travelled horizontally while it was in the air, and hence how far it got hit.

John E. Franklin · 2008-07-31 12:31:14

also, for curiosity, take 32 ft/s^2 on earth, and half of that is 16, and 16 / 2.66 = 6.01503759
That is because the moons gravity is 6 times less than earth.
I used 16 instead of 32 because I recalled your formula: y = upwardSpeed t - 16t^2, half of 32, due to calculus stuff.
Your upward speed is .707 times 88 in feet/second because .707 is about sin45degrees.
Good Luck.

kwinrow · 2008-07-31 16:07:16

these for the values I got for t using the quadratic formula:

t=0, and t is approx. 18.07

then i plugged 18.07 into the first equation and got:

approx. 1124.41

this is right? is this the answer?oh yeah, what units would i use?

mathsyperson · 2008-08-01 01:17:17

When I solve the quadratic, I get 0 or ~23.39 seconds. I'm not sure how you got to your answer.
You've done the second bit right though (as in, if your time was right then that's what the distance would be).

v is given in ft/sec, so the final answer will be in feet.

kwinrow · 2008-08-01 01:41:39

one other question, would I have to convert the answer to feet?

mathsyperson · 2008-08-01 02:02:37

No, the answer is already in feet. I thought that's what you were asking.

John E. Franklin · 2008-08-01 02:03:07

y is in feet and x is in feet, so your all set.

(feet=y) = (vsintheata=feet/sec)(t=sec) - (2.66=Half_of_acceleration=feet/(sec*sec))(t*t=sec*sec) + (feet=h)

It might not look like everything is in feet, but the dividing by seconds is always multiplied by seconds,
so the seconds disappear and turn into 1. You will learn about "units" really well in a chemistry course,
because of the interesting formulas there.

kwinrow · 2008-08-01 02:45:42

ok thanks a lot

Math Is Fun Forum

#1 2008-07-31 09:08:28

help on problem

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Re: help on problem

#3 2008-07-31 12:31:14

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#5 2008-08-01 01:17:17

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