00:01
Problem we have the following setup suppose this is the ground level and we have this person a golfer who hits a golf ball from this point so it will have some initial speed making this angle let's say theta from the horizontal so it will follow this trajectory this point is a and we have the gravitational acceleration g so the initial speed is given to be 50 meters per second.
00:41
This angle is given to be 25 degrees and g is 9 .8 meters per second square.
00:49
With that we are going to determine the radius of curvature of the trajectory at this initial point a and also at the highest point of the trajectory.
01:03
Okay now let us assume this is x and upper this y so that origin with the initial position of the object.
01:15
Along x we have constant velocity motion.
01:19
So we have x equal to x0 plus x component of the initial velocity times t.
01:25
We have here x0 equal to 0 and v0 x is v0 cosine, and we have t.
01:34
So if you plug in the numbers, we are going to obtain 45 .315.
01:44
4t.
01:45
Along y we have constant acceleration motion.
01:49
So we can write y0 plus y component of the initial velocity times t plus one half acceleration t squared.
01:59
Y 0 is 0 v0 y0 is v0 sine theta and g is a is minus g.
02:11
Okay now if you plug in the numbers we are going to obtain 21 .139 t minus 4 .9 t squared.
02:24
Now in the calculations of the radius of curvature we don't need time.
02:29
So let's get rid of t using first equation...