Projectile motion when you are only given time and range

[Acmnji]

Homework Statement

I am very lost and would love help. Given in the description is;"A golf ball leaves a golf club at an angel 30 degrees above the horizontal and lands on the green 150 meters away initial position." With this information i am supposed to find the balls initial velocity, how long it was in the air and how high it rises

The Attempt at a Solution

to find the initial velocity i did delta r = [vi^2 * Sin (60) ]/ 9.81 = 41.22.
not 100% sure this is correct but its what i have so far and i have no idea where to go from here

 

[cnh1995]

Homework Statement

I am very lost and would love help. Given in the description is;"A golf ball leaves a golf club at an angel 30 degrees above the horizontal and lands on the green 150 meters away initial position." With this information i am supposed to find the balls initial velocity, how long it was in the air and how high it rises

The Attempt at a Solution

to find the initial velocity i did delta r = [vi^2 * Sin (60) ]/ 9.81 = 41.22.
not 100% sure this is correct but its what i have so far and i have no idea where to go from here

Your calculation of initial velocity is correct.

You need to find the time of flight (T) and maximum height (H). Do your notes contain the formulas for T and H ?

 

[Acmnji]

Your calculation of initial velocity is correct.

You need to find the time of flight (T) and maximum height (H). Do your notes contain the formulas for T and H ?

okay thanks and they don't contain either of those formulas and i don't see either in my notes as well.

 

[cnh1995]

okay thanks and they don't contain either of those formulas and i don't see either in my notes as well.

Well, that's odd!

Anyway, you can look them up or you can derive them on your own if you applied your knowledge of vectors and kinematic equations.
What are the x and y components of initial velocity? What is the acceleration in x and y directions?

 

[Acmnji]

for the x and y components of vi would it be 41.22cos30 and 41.22sin30?

 

[cnh1995]

for the x and y components of vi would it be 41.22cos30 and 41.22sin30?

Yes.
What about acceleration?

 

[Acmnji]

no acceleration in the x and a acceleration of -9.81 in the y?

 

[cnh1995]

no acceleration in the x and a acceleration of -9.81 in the y?

Correct.
Can you write the relevant kinematic equations for finding T and H?

 

[Acmnji]

im sorry but i have no clue and I am not able to find it anywhere.

 

[cnh1995]

im sorry but i have no clue and I am not able to find it anywhere.

What is the horizontal dispalcement? Which component of velocity is responsible for it?

 

[Acmnji]

vix and time dictate horizontal displacement

 

[cnh1995]

vix and time dictate horizontal displacement

Yes.
So you can find time from this. You know Vx and horizontal displacement.

 

[Acmnji]

So if the horizontal displacement is 150 and the vx is 35.7 it would be 150/35.7=time=4.2 seconds?

 

[cnh1995]

So if the horizontal displacement is 150 and the vx is 35.7 it would be 150/35.7=time=4.2 seconds?

Yes.

 

[Acmnji]

and the equation for height, would that be vy + (0.5*9.81*4.2^2) ?

 

[cnh1995]

and the equation for height, would that be vy + (0.5*9.81*4.2^2) ?

Careful there..
At what time will the ball be at the maximum height?

 

[Acmnji]

at half the time so 2.1 seconds?

 

[cnh1995]

at half the time so 2.1 seconds?

Right.

 

[Acmnji]

im confused now, how would that change the equation

 

[cnh1995]

vy + (0.5*9.81*4.2^2) ?

You have taken t=4.2s..

 

[Acmnji]

so then would it change to vy + (0.5*9.81*2.1^2)

 

[Inventive]

Ok. Would you have access to a graphing calculator compare the path of the golf ball to your answer?