Question

A ball of mass m = 1.6 kg is fired at angle of 42° with respect to the horizontal, at an initial speed v1 = 14.0 m/s. the ball achieves a maximum height h = 4.4 m after traveling a horizontal distance d = 9.7 m and speed v = 10.43 m/s. what is the z- component of the angular momentum of ball at this instance, with respect to an axis passing through x, located at the point where the cannonball will land? magnitude of acceleration due to gravity is 10 m/s²

A) 1.6 kg⋅m/s²

B) 0 kg⋅m/s²

C) 3.2 kg⋅m/s²

D) −3.2 kg⋅m/s²

Answer 1

The z-component of the angular momentum of the ball at this instance is 108.92 kg·m/s.

Step-by-step explanation:

To find the z-component of the angular momentum of the ball at this instance, we first need to calculate the velocity component in the z-direction. The z-component of the velocity can be calculated using the formula:

vz = v * sin(theta)

where vz is the z-component of velocity, v is the magnitude of the velocity, and theta is the angle at which the ball was fired. Substituting the given values into the formula:

vz = 10.43 m/s * sin(42°) = 7.08 m/s

The z-component of the angular momentum can then be calculated using the formula:

Lz = m * vz * d

where Lz is the z-component of angular momentum, m is the mass of the ball, vz is the z-component of velocity, and d is the horizontal distance traveled by the ball. Substituting the given values into the formula:

Lz = 1.6 kg * 7.08 m/s * 9.7 m = 108.92 kg·m/s

Therefore, the z-component of the angular momentum of the ball at this instance is 108.92 kg·m/s.