2 Projectiles are fired simultaneously

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In summary, two projectiles are fired simultaneously with the same initial speed from ground level and cover the same horizontal distance of 160m. One projectile reaches the ground 6 seconds earlier than the other. The only force acting on both projectiles is gravitational acceleration (g = 10m/s^2). To calculate the initial speed (u), we can use the equations Range = u^2 sin 2theta/g and Time = 2u sin theta/g, where u is the initial velocity, theta is the angle of projection, and T is the time taken by the projectile to reach the ground. Using trigonometry, we can set up the equation T = t + 6 and solve for u.
  • #1
Om Swostik

Homework Statement


2 projectiles are fired simultaneously from ground level with same initial speed (u).Both cover same horizontal distance of 160m on reaching the ground level .One of them reaches 6 sec prior to the other.Only gravitational acceleration g=10m/s squared governs the motion of both the projectile.Calculate u.[/B]

Homework Equations


Range(horizontal distance)=u squared sin 2×theta/g= Ux cos theta ×time
Time=2u sin theta/g
Where ,
U is initial velocity
Theta is the angle of projection
and T is the time taken by the projectile to reach ground level.
Note:vector u has 2 components which are Ux=u cos theta and Uy=u sin theta

The Attempt at a Solution

 
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  • #2
Om Swostik said:

Homework Statement


2 projectiles are fired simultaneously from ground level with same initial speed (u).Both cover same horizontal distance of 160m on reaching the ground level .One of them reaches 6 sec prior to the other.Only gravitational acceleration g=10m/s squared governs the motion of both the projectile.Calculate u.[/B]

Homework Equations


Range(horizontal distance)=u squared sin 2×theta/g= Ux cos theta ×time
Time=2u sin theta/g
Where ,
U is initial velocity
Theta is the angle of projection
and T is the time taken by the projectile to reach ground level.
Note:vector u has 2 components which are Ux=u cos theta and Uy=u sin theta

The Attempt at a Solution

An attempt is required. Forum rules.
 
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  • #3
THE ATTEMPT AT A SOLUTION:
I took the angle of projection of 1st projectile as theta and the angle of the 2nd one as 90 - theta (as there can be two angles of projection for the same range).
I equated the range and the time ,that is
T=t+6.As I have really limited knowledge of trigonometry, the resulting equation which I arrived at couldn't be solved by me.
 
  • #4
Om Swostik said:
THE ATTEMPT AT A SOLUTION:
I took the angle of projection of 1st projectile as theta and the angle of the 2nd one as 90 - theta (as there can be two angles of projection for the same range).
I equated the range and the time ,that is
T=t+6.As I have really limited knowledge of trigonometry, the resulting equation which I arrived at couldn't be solved by me.
Please post the equation. It might save time to post your working too, in case you have a mistake somewhere.
 

1. How can two projectiles be fired simultaneously?

Two projectiles can be fired simultaneously by using two separate launch mechanisms, such as two guns or two catapults, or by using one launch mechanism that can fire multiple projectiles at once.

2. Will the projectiles have the same initial velocity?

In most cases, yes, the projectiles will have the same initial velocity if they are fired simultaneously from the same launch mechanism. However, if there are any external factors, such as wind or uneven launch, the initial velocities may differ slightly.

3. What factors affect the trajectory of the projectiles?

The trajectory of the projectiles can be affected by several factors, including the initial velocity, angle of launch, air resistance, and gravitational pull. Other external factors, such as wind and temperature, can also impact the trajectory.

4. Can the projectiles collide with each other?

It is possible for the projectiles to collide with each other if they are fired at close range and have similar trajectories. However, in most cases, the projectiles will follow their own individual paths and not collide with each other.

5. How can the distance between the two projectiles be calculated?

The distance between the two projectiles can be calculated using the distance formula, which takes into account the initial velocity, angle of launch, and time of flight for each projectile. This formula can be used to find the horizontal distance between the two projectiles at any given time.

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