# Projectile motion when you are only given time and range

Tags:
1. Mar 13, 2017

### Acmnji

1. The problem statement, all variables and given/known data
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

3. 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

2. Mar 13, 2017

### cnh1995

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 ?

3. Mar 13, 2017

### Acmnji

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

4. Mar 13, 2017

### cnh1995

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?

5. Mar 13, 2017

### Acmnji

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

6. Mar 13, 2017

### cnh1995

Yes.

7. Mar 13, 2017

### Acmnji

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

8. Mar 13, 2017

### cnh1995

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

9. Mar 13, 2017

### Acmnji

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

10. Mar 13, 2017

### cnh1995

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

11. Mar 13, 2017

### Acmnji

vix and time dictate horizontal displacement

12. Mar 13, 2017

### cnh1995

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

13. Mar 13, 2017

### Acmnji

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

14. Mar 13, 2017

### cnh1995

Yes.

15. Mar 13, 2017

### Acmnji

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

16. Mar 13, 2017

### cnh1995

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

17. Mar 13, 2017

### Acmnji

at half the time so 2.1 seconds?

18. Mar 13, 2017

### cnh1995

Right.

19. Mar 13, 2017

### Acmnji

im confused now, how would that change the equation

20. Mar 13, 2017

### cnh1995

You have taken t=4.2s..