Kinematics -- Projectile motion problem

In summary, the students were discussing a problem involving two guns, Gun A and Gun B, that were fired at varying time intervals from a height of 10 meters above the ground. They were asked to calculate which gun was fired first and the displacement and time at which the two bullets would collide. The students had different approaches to solving the problem and eventually determined that without knowing the initial velocity or time, a solution could not be found. However, when the initial velocity of 5√3 m/s was given, a solution was possible.
  • #1
MARK 42
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0
Poster has been reminded to use the HH Template and show their work toward a solution
One bullet was fired from Gun A and Gun B each at varying time interval. Both the guns are 10 meters above the ground. Calculate: a) Which gun was fired first. b) Displacement and time at which the two bullets will collide.
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  • #2
What have you done so far? Just the vertical displacement? Or, both vertical and horizontal displacements?
 
  • #3
First off, you did not use the template. Please do.
Secondly, you have not shown your efforts yet.
Lastly, you should be able to answer at least part a based on your intuition. I guess the assumption is that the firing velocity of both guns is equal.
 
  • #4
Oh, sorry.
If we consider time as 'T' then by traditionally solving, I got Ta = 1/2Tb. I don't know what to do further. The final answer is 1 second.
And the displacements, I got Sy for A=Sy for B.
 
  • #5
1 second for Ta or Tb?
I am guessing that trajectory a starts completely horizontal, and b is at 60 degree elevation from horizontal.

Next, you should relate the y displacement positions at the final time:
## v\frac{\sqrt{3}}{2}T_f - \frac{9.8}{2}(T_f)^2 = - \frac{9.8}{2}\left(\frac{T_f}{2}\right)^2##

I don't immediately see how you can find a solution without some dependence on initial velocity, unless you knew T_f =1 sec from the start.
 
  • #6
Exactly. I feel the same. I think the question somehow lacks specifications with respect to both velocity and time.
Anyways, thanks for your help.
 
  • #7
I can confirm that you need one of them. Otherwise doubling the velocity and the time difference for a solution scales everything up and leads to a new solution.
 
  • #8
What if we consider initial velocity = 0? Assuming the calculation starts from the point the bullets were at rest?
 
  • #9
You can't have a horizontal motion or a 60° angle if you release the bullets at rest. Also, they will never meet then.

Actually, I wonder why the 10 meters are given, they don't seem relevant.
If you assume that the bullets hit each other at the same time they hit the ground, the problem gets a unique solution (assuming the initial velocities are the same).
 
  • #10
Our teachers modified the question giving us the velocity as 5√3 m/s. Would that work?
 
  • #12
Did you find a solution?
 

What is projectile motion?

Projectile motion refers to the movement of an object in a curved path under the influence of gravity. It occurs when an object is given an initial velocity and then allowed to freely move under the force of gravity.

What is the difference between projectile motion and regular motion?

The main difference between projectile motion and regular motion is the presence of an external force acting upon the object. In regular motion, the object is typically moving in a straight line at a constant speed. In projectile motion, the object is moving in a curved path due to the force of gravity.

What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by its initial velocity, the angle at which it is launched, and the force of gravity. Other factors such as air resistance and wind can also have an impact on the trajectory.

How do you calculate the range of a projectile?

The range of a projectile is the horizontal distance it travels before hitting the ground. It can be calculated using the formula R = V02 * sin(2θ) / g, where R is the range, V0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

How does the launch angle affect the range of a projectile?

The launch angle has a significant impact on the range of a projectile. The range will be at its maximum when the launch angle is 45 degrees, as this gives the projectile an equal amount of horizontal and vertical velocity. Launching at angles higher or lower than 45 degrees will result in a shorter range.

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