# A trajectory problem

1. Mar 9, 2006

### raizen91

hello guys! i find physics really difficult and my classmates and i have been dumbfounded by this problem. hope you could help me with the formulas i should use and how is should use them. this is was the first problem: ooops..this problem aint a trajectory problem. its a projectile motion problem. pls help, i dont know what our teacher expect from us 10 year olds grade school students...sigh

a baseball is batted into the air and caught at a point 100m distant horizontally in 4 seconds. if air resistance is neglected, what is its maximum height in meters above the ground? thnx

Last edited: Mar 9, 2006
2. Mar 9, 2006

### Harmony

May I know if the angle of the projectile motion is given?

3. Mar 9, 2006

### GregA

You are looking for the distance an object will travel such that the vertical component of it's velocity = 0 at a certain point in time

Do you know at what time the ball will reach it's greatest height?

Do you know what force will cause the ball to achieve a (vertical) speed of 0m/s from v m/s?

Last edited: Mar 9, 2006
4. Mar 9, 2006

### vaishakh

The given information is certianly insufficient.

5. Mar 9, 2006

### GregA

I disagree...given that the ball is caught at the same height as it was thrown (one would reasonably assume) we can infer the time at which it is at its greatest height..if we really wanted to we could also find its speed because wecan find not only the vertical component of its initial velocity but also the horizontal too...and finally with this we can find the angle of projection.

All that is needed though is the distance the ball will travel before it starts to fall back down again.

6. Mar 9, 2006

### vaishakh

Sorry. I misread the question. Okay to assume that ball is caught at the same height at which it is shot is something which need not be said. However I didn't see the 4 seconds time given.
So you know horizontal component as well as vertical component and can certianly calculate the initial velocit as well as projection anlge.
Very Very Sorry.

7. Mar 9, 2006

### Harmony

Is the answer 125m? (assuming g=10ms^-2)
1. Horizantal velocity = horizantal distance / time
2. Vertical velocity =( horizantal velocity / cos x (x=angle) ) * sin x
3. sinx/cosx=tan x (trigonometry)
3. Vertical velocity = horizantal velocity * tan x
4. Since v^2=u^2-2gh, v=0,
5. (vertical velocity)^2=2gh
6. To get the highest value of h, x must be 45 degrees. (tan45=1)
7. Calculate the height now.

8. Mar 9, 2006

### tony873004

10 years old? You were given this problem in the 3rd or 4th grade?

9. Mar 10, 2006

### raizen91

sorry...that's all the info our teacher gave us. my classmates and i had the same prob... like no angle???

10. Mar 10, 2006

### raizen91

yap im ten..but im in my 5th grade. i find it quite silly when our teacher thinks that we're smart enough to answer questions as difficult as this..

11. Mar 10, 2006

### raizen91

let me try that harmony...hmmm....tnx

12. Mar 10, 2006

### andrevdh

The launch angle $\theta_o$ can be calculated via the 4s for an object to fall from rest downwards to the point where the ball is catched
"[PLAIN [Broken] Forums/projectile launch angle.htm"]http://mysite.mweb.co.za/residents/andriesvdh/Physics [Broken] Forums/projectile launch angle.htm[/URL]

Since $v_x=25\ m/s$
it follows that the initial upwards velocity is given by
$v_{yo}=25\times0.784$

Last edited by a moderator: May 2, 2017
13. Mar 10, 2006

### HallsofIvy

Staff Emeritus
Actually, there is more information than necessary! That "100 m" is not necessary. It's also not necessary to worry about the angle. You have two separate equations for the horizontal and vertical distances.

horizontal: x= vxt
vertical: y= -4.9t2+ vyt

Since the ball moves 100 m horizontally, in 4 seconds, we have
100= 4vx and 0= -4.9(16)+ 4vy.

We really only need the second equation: 78.4+ 4vy= 0 can be solved for vy. After you know that you can find the maximum height by completing the square in y= -4.9t2+ vyt.

If the ball were hit straight up and came back down to the same level in 4 seconds or hit so that it went 1000m horizontally while coming back to the same level in 4 seconds, it would still have the same maximum height.

14. Mar 10, 2006

### raizen91

will the answer be 19.6? i dunno about ur formula but i have used a different approach. since the the time is 4 sec., i would assume that the ball will reach its highest point at 2 sec. so i used two formulas which is
v^2 = v0^2+ 2as and
v = v0 + at
so
0 = vo + (-9.8)(2)
vo = 19.6 m/s
0= (19.6)2 + 2 (-9.8)s
-(19.6)2/-19.6 = -19.6s/-19.6
s= 19.6
this is my final answer..19.6 being the displacement

15. Mar 10, 2006

### Haxx0rm4ster

lol he is either 15 or 14.
Inferring that the 91 in his name is the year when he was born.

16. Mar 11, 2006

### andrevdh

Yes raizen you've got it! Note that my $v_{yo}$ comes to the same as yours.

17. Mar 11, 2006

### raizen91

:tongue2: ......................

18. Mar 11, 2006

### raizen91

tnx for the help!!!

19. Mar 11, 2006

### andrevdh

It's a pleasure.

20. Mar 13, 2006

### raizen91

i got two more problems, hope you could help. more projectile problems...(sigh), i dunno how to start, hoping you guys could help me with the initial steps...

1. a missile is fired with a launch velocity of 15,000 ft/s at a target 1,200 miles away. at what angle must it be fired to hit the target? how long after it is fired will the target be hit.

2. a projectile is fired at an angle of 30 degrees above the horizontal from the top of a cliff 600 ft. high : the initial speed of the projectile is 2000 ft/s. how far will the projectile move horizontally before it hits level grained at the base of the cliff?

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