Finding Initial Velocity: Projectile Motion Problem

In summary, the conversation discusses the motion of a particle projected on a horizontal ground under gravity with an initial velocity of 2u in the horizontal direction and u in the vertical direction. The particle lands at a distance of 80m from the point of projection and it is shown that u=14. However, there is a discrepancy in the calculations and it is asked where the mistake may have been made. After considering the equations for motion in the horizontal and vertical planes, it is determined that the mistake may be in the substitution of values, leading to an incorrect value of u.
  • #1
brandon26
107
0
A particle is projected on a horizontal ground and moves freely under gravity.
The horizontal and vertical components of the initial velocity are 2u and u ms^1 respectively.

The ball lands a distance 80m from the point of projection.

Show that u=14

This is what I did:

Taking motion in the horizontal plane------

2u = 80/t

Taking motion in the vertical plane-----

displacement (s) =0
acceleration (a)= -9.8
initial velocity (u) = u
time of motion (t) = t

therefore using s=ut +(1/2)at^2

I get: 4.9t=u

substituting this into the first equation should give me the correct value of u, but it doesnt. Can someone tell me where i went wrong?
:confused: :confused:
 
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  • #2
[tex] 0 = ut - 4.9t^2 [/tex]
Assuming that t is non-zero, since that is an obvious solution, [tex] t = \frac{2u}{g} [/tex], therefore, since velocity in the horzontial plane is constant, [tex]4u^2 = 80g [/tex], then solve that
 
  • #3
Why doesn't it? If u= 4.9 t, then t= u/4.9. Putting that into
2u= 80/t, 2u= (80)(4.9)/u so u2= 40(4.9). What do you think that is?
 

Related to Finding Initial Velocity: Projectile Motion Problem

1. What is initial velocity in projectile motion?

Initial velocity, also known as the launch velocity, is the velocity at which an object starts moving in a projectile motion. It is the speed and direction at which the object is launched.

2. How do you find initial velocity in a projectile motion problem?

To find the initial velocity in a projectile motion problem, you need to know the object's horizontal and vertical displacements, time of flight, and acceleration due to gravity. You can then use the equation v = d/t to calculate the initial velocity in the horizontal direction, and the equation v = u + at to calculate the initial velocity in the vertical direction.

3. What is the difference between initial velocity and final velocity in projectile motion?

Initial velocity is the velocity at the beginning of the motion, while final velocity is the velocity at the end of the motion. In projectile motion, initial velocity refers to the velocity at which the object was launched, while final velocity refers to the velocity at which the object hits the ground or reaches its highest point.

4. How does initial velocity affect the trajectory of a projectile?

The initial velocity has a significant impact on the trajectory of a projectile. It determines the speed at which the object moves and the angle at which it is launched, which both affect the shape and height of the projectile's trajectory. A higher initial velocity results in a longer and higher trajectory, while a lower initial velocity results in a shorter and lower trajectory.

5. Can the initial velocity of a projectile be negative?

Yes, the initial velocity of a projectile can be negative. This means that the object is launched in the opposite direction of the positive x-axis. The negative sign indicates that the object is moving in the negative direction, not that the velocity is decreasing.

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