Solve Golf Ball Trajectory: Time, Max Height, Distance, and Final Velocity

[pooface]

TEST question!

Homework Statement

Golf ball is struck at 12 m above the plain of a tee giving it a velocity of 40m/s at an angle of 30degrees.

a) find the time of flight
b) find max height above plane
c) horizontal distance to point of landing.
d) final velocity and angle.

Homework Equations

The Attempt at a Solution

Vox = 40cos30
Voy = 40sin30

a) -12 = 40sin30t + 0.5(-g)t^2
t=4.6084 seconds

b) disregarding the 12m elevation (which i will add later on).
0=40sin30t + 0.5(-g)t^2
t=4.0775s
t/2 = time at peak
y= - 0.5(-g)t^2 +12
= 32.387m

c)x =voxt
= 34.34(4.6084)
=158.25m

d)
-12= Vfy(4.6084) -0.5(-g)(4.6084)^2
Vfy = 25.21m/s
angle = arctan(vfy/vox) = -36.28deg

 

[catkin]

What is your question?

 

[pooface]

the a),b),c),d)

 

[catkin]

That's not a question.

What do you want?

 

[pooface]

What i meant was, confirmation of process.

Have i done this correctly? I want to check because I want to see if I screwed up a test question.
Thanks.

 

[Kurdt]

I'd have a look at b again. You can't assume that the maximum height comes at half the flight time because of the difference in elevation from where it was hit and where it lands.

I'd also try part d again. The velocity in the formula you're using there is an initial velocity.

 

[pooface]

part b) what i did was I neglected the initial height because i want to calculate the time of impact then half that time. Using this time, I get the height. but i would have to add the 12m back to get the real height.

I also could have used

Vfy=Voy+at

0=-20+(-9.81)t

which equals the same 2.039s.

part d) since vox is constant the final would be the same as well. so i just thought i would still name it vox.

 

[pinkyjoshi65]

Hey, I got a question. Isint this just direct applcations of projectile formulas.
Like: DeltaT= 2ViSintheta/g and so on?

 

[learningphysics]

Everything looks right to me except b). d) is correct... but a couple of little things are there...

For b), they want the height above the plane... not the height above the ground... so you wouldn't add 12...

also, you want: d = v1*t + (1/2)at^2 = 40sin30t + 0.5(-g)t^2... plug in t = 4.0755/2 will work.. gives 20.408m

you can also use: v2^2 = v1^2 + 2ad. v2 = 0, v1 = 40sin(30). so d = 40^2[sin(30)]^2/(2g) = 20.408m

Kurdt, the formula being used in part d, is d = vf*t - (1/2)at^2 which is a correct formula.

In part d, your Vfy should be -25.21 which is probably what you meant. So the final speed is sqrt[(-25.21)^2 + (34.34)^2] = 42.6 m/s. and the angle is right -36.28 degrees. ie: 36.28 degrees below the horizontal