A body is projectedat an angle 30 degree with the horizontal with the momentum p. At its highest point the magnitude of the momentum is?

Question

Answer

Answer

Answer

[(3)^1/2]/2*P

Answer

Projectile motion and momentum:
Projectile motion refers to the motion of an object that is launched into the air and follows a curved trajectory under the influence of gravity. Momentum is defined as the product of an object's mass and velocity, and it is a vector quantity. In projectile motion, the momentum of the object changes as it moves through the air due to changes in its velocity.

Given information:
- The body is projected at an angle of 30 degrees with the horizontal.
- The momentum of the body is given as 'p'.

Analysis:
To find the magnitude of the momentum at the highest point, we need to understand the motion of the projectile and how the momentum changes during this motion.

1. Initial momentum:
When the body is launched, it has an initial momentum that can be resolved into horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component changes due to the influence of gravity.

2. Vertical motion:
The vertical motion of the projectile can be analyzed separately from the horizontal motion. At the highest point of the trajectory, the vertical component of velocity becomes zero, while the horizontal component remains constant.

3. Momentum at the highest point:
At the highest point, the body momentarily comes to rest in the vertical direction. However, its horizontal velocity remains constant. Therefore, the magnitude of the momentum at the highest point is equal to the magnitude of the horizontal component of momentum at the start.

4. Resolving the momentum:
To find the magnitude of the momentum at the highest point, we can resolve the initial momentum into horizontal and vertical components. The horizontal component can be found using the formula:
Momentum in the horizontal direction = initial momentum * cos(angle)

5. Calculating the magnitude:
Since the horizontal component of momentum remains constant throughout the motion, the magnitude of momentum at the highest point is equal to the magnitude of the horizontal component of momentum at the start.

Conclusion:
The magnitude of the momentum at the highest point of the projectile's trajectory is equal to the magnitude of the horizontal component of momentum at the start. By resolving the initial momentum into horizontal and vertical components, we can calculate the magnitude of the momentum at the highest point.

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