Body of mass M is thrown with velocity V making an angle 45 degree with horizontal. The magnitude of change in momentum between starting point at and maximum height is?

Question

Answer

Change in momentum= M (change in velocity).
as initial velocity = v cos theta i^ + vsin theta j^. & velocity at highest point = v cos theta i^. since overall change in velocity = v sin theta j^ = v sin 45= v / sqrt.2. & change in momentum = Mv/ sqrt.2. j^

Answer

@maxi height horizontal velocity of the body is zero, so change in momentum along x is zero. whereas along y change in momentum=MV-MVsin45=MV-MV(.707)=.293MV

Answer

Change in Momentum

To find the change in momentum, we first need to determine the momentum at the starting point and the momentum at the maximum height.

Momentum at Starting Point

The momentum at the starting point can be calculated using the formula:

Momentum = mass * velocity

Given that the mass of the body is M and the velocity is V, the momentum at the starting point is:

Momentum at starting point = M * V

Momentum at Maximum Height

To find the momentum at the maximum height, we need to consider the vertical and horizontal components of the velocity separately.

Vertical Component of Velocity

The vertical component of the velocity can be calculated using the formula:

Vertical velocity = velocity * sin(angle)

In this case, the angle is given as 45 degrees. Therefore, the vertical component of the velocity is:

Vertical velocity = V * sin(45°) = V * (1/√2)

Horizontal Component of Velocity

The horizontal component of the velocity can be calculated using the formula:

Horizontal velocity = velocity * cos(angle)

In this case, the angle is given as 45 degrees. Therefore, the horizontal component of the velocity is:

Horizontal velocity = V * cos(45°) = V * (1/√2)

Momentum at Maximum Height

The momentum at the maximum height can be calculated by considering the vertical component of the velocity. Since the body reaches its maximum height, the vertical component of the velocity becomes zero. Therefore, the momentum at the maximum height is:

Momentum at maximum height = M * Vertical velocity = M * V * (1/√2)

Change in Momentum

The change in momentum is the difference between the momentum at the starting point and the momentum at the maximum height. Therefore, the change in momentum is:

Change in momentum = Momentum at maximum height - Momentum at starting point

Change in momentum = M * V * (1/√2) - M * V

Simplifying the equation, we get:

Change in momentum = M * V * (1/√2 - 1)

This is the magnitude of the change in momentum between the starting point and the maximum height.

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