Question

A golfer stands 390 ft away from the hole and 40 ft below the hole. Assuming the ball is hit with an initial speed of 150 ft/s at what angle should it be hit to land in the hole.

Answer 1

he just needs the help of God

Answer 2

did they provide solution?

Answer 3

i'm guessing 23.34 degrees or 72.51 degrees

Answer 4

yes

Answer 5

So Im assuming I should start from a(t) = <0, -32> ft/sec

Answer 6

Then take Integral of that to get v(t) which would be v(t) = <0, -32t> but needs to satisy the initial speed condition

Answer 7

calculus? I just used simple algebra

Answer 8

150sinA gives the vertical force upwards
using the height function which factors in force of gravity
let initial height be -40

h(t) = -16t^2 + (150sinA)t - 40 = 0

then use 150cosA as horizontal force
x(t) = (150cosA)t = 390

--> A = arccos(390/150t)

Answer 9

Yes

Answer 10

@sourwing can you show your work or explain how you obtained your answer

Answer 11

So What Im curious about is I think my reasoning to get v(t) was correct.......but when I take an integral again can I treat sin and cos as if they were a constant?

Answer 12

exactly the same way you did. @dumbcow , except I solved for t, and plug it in h(t)

Answer 13

oh lol yeah that would be easier
anyway i assumed so but for the benefit of @jasonjohnson86 a more detailed solution should be given

Answer 14

well, I wasn't sure of my answer. That's why I asked him if the solution was provided.

Answer 15

Ok this all helps. But I would like help with the calculus approach. I have a(t) = to the vector <0, -32> and then taking the integral v(t) = <0, -32t> a some vector C that satisfies inital conditions...therefore v(t) = <150costheta, 150sintheta - 32t>

Answer 16

So When I then take the integral of v(t) can I treat sin and ccos as if they were constats so that the integral of v(t) = r(t) = <150tcos(theta), 150sin(theta) - 16t^2>?

Answer 17

yes you are correct, they are constants because you are integrating with respect to "t" not the angle

Answer 18

ahhhhhhhhhhhhh thank you lol! That makes perfect sense. And I totally feel dumb didn;t even think of the algebra approach.

Answer 19

well you still have to do the algebra...the calculus only gives you the position vectors/equations
however in physics those are just standard formulas so you dont have to do the calculus to derive them every time :)

Answer 20

now the question is, will the golfer make it? XD

Answer 21

he probably won't. He needs the help of God XDD

Answer 22

But then, again God isn't that interested in golf lol

Answer 23

agreed, even if it hit the hole it would prob bounce out or ricochet off the pin