Finding Maximum Height and Initial Velocity when only given angle and distance

In summary, the problem involves a circus performer being shot out of a cannon and passing over a net placed 6 meters horizontally from the cannon. When the cannon is aimed at an angle of 40 degrees above the horizontal, the performer barely clears the net. The task is to find the muzzle speed of the cannon and the height of the net. The solution involves using equations for both the x and y directions separately, with accelerations of 0 and -g respectively. The initial speed of the performer is represented by v, which can be solved for in both the x and y direction equations. The equation for the y direction involves v^2 = (v)(cos 40) + 2 (-9.8) (6),
  • #1
uncertain22
5
0

Homework Statement



A Circus performer is shot our of a cannon and shot over a net that is placed horizontally 6 meters from the cannon. When the cannon is aimed at an angle of 40 degrees above the horizontal, the performer is moving in the horizontal direction and just barely clears the net as he passes over it. What is the muzzle speed of the cannon and how high is the net?


Homework Equations


I have no idea, which is the problem



The Attempt at a Solution



assuming that R (sub) x is 6 I tried using the tan to solve for the hyp and then the maximum height but that was the wrong answer

I can't seem ti figure out how to find the velocity becasue all of the equations i have need the time
 
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  • #2
welcome to pf!

hi uncertain22! welcome to pf! :wink:

in all these projectile problems, you need to do equations for the x and y directions separately (with accelerations 0 and -g, respectively) …

call the time "t", choose one of the standard constant acceleration equations for each direction, and solve …

what do you get? :smile:
 
  • #3
I tried doing it in the x and y directions seperatley but I don't know how to figure out the Velocity in the x and y directions without having an original velocity to go with.

I tried doing the distance in the x and y directions in case that would help me somehow but it just kept coming out wrong

Also, what does u stand for in the acceleration equations?
 
  • #4
hi uncertain22! :wink:
uncertain22 said:
I tried doing it in the x and y directions seperatley but I don't know how to figure out the Velocity in the x and y directions without having an original velocity to go with.

call the initial speed v …

now show us your equations :smile:

(u in s = ut + at2/2 is the initial speed in that direction)
 
  • #5
v^2 = (v)(cos 40) + 2 (-9.8) (6)

i don't think that is right at all though
and I don't know if 6 is even correct I feel like I need to put it into x and y components I just don't know how
 
  • #6
woops I think the (v times the cos of 40) is supposed to be squared too, I just forgot to type it in
 
  • #7
(try using the X2 icon just above the Reply box :wink:)

that's certainly a possible equation for the y-direction …

what would it mean? what would v be in this case? why is it useful?

(the 6 must be wrong, btw, it's a horizontal distance, and this is a vertical equation :redface:)

try a different vertical equation if that one won't work

(and then you'll need a horizontal equation also)

(i'm going to bed now, so someone else will have to take over :zzz: …)
 
  • #8
how do I know which equations are vertical and which are horizontal?
 
  • #9
hi uncertain22! :wink:

(just got up :zzz: …)
uncertain22 said:
how do I know which equations are vertical and which are horizontal?

well, they're your equations … you can make whatever equations you want :smile:

in the vertical direction, you need the standard constant acceleration equations, with a = -g

in the horizontal direction, a is 0, so you can just use the standard constant velocity equation :wink:

show us what you get :smile:
 

1. How can I find the maximum height of a projectile when only given the angle and distance?

The maximum height of a projectile can be calculated using the equation h = (v02sin2θ)/2g, where v0 is the initial velocity, θ is the angle, and g is the acceleration due to gravity. Plug in the given values and solve for h to find the maximum height.

2. Is there a way to find the initial velocity of a projectile when only given the angle and distance?

Yes, the initial velocity can be found using the equation v0 = d/(cosθ√(2h/g)), where d is the distance traveled and h is the maximum height. Plug in the given values and solve for v0 to find the initial velocity.

3. Can I use these equations for any projectile motion, regardless of the initial velocity?

Yes, these equations can be used for any projectile motion, as long as the initial velocity, angle, and distance are known. However, they assume that there is no air resistance.

4. What units should I use for the distance and angle in these equations?

The distance should be measured in meters (m) and the angle should be measured in degrees (°). Make sure to convert any other units to these measurements before plugging them into the equations.

5. Are there any other factors that could affect the accuracy of these calculations?

Yes, these calculations assume that there is no air resistance and that the acceleration due to gravity is constant. In reality, air resistance and changes in gravity could affect the accuracy of these calculations. Additionally, any errors in measurement or calculation could also impact the accuracy of the results.

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