1.A tall pole and a short pole (both having the same diameter and mass density) are both standing straight up. Both are allowed to tip and fall, starting from rest, at the same time. Which reaches the ground first?

2.When a non-vertical projectile strikes the ground, which part of the momentum of the projectile is conserved during the collision?

The torque on each is massdensity*h*gh/2 or

T=massdensity*g*h^2/2
of course, h is different.

angular acceleration is Torque/momentinertial
where momentinertia=massdensity*h*h^3/3

angular acceleartion= k/h^2

so, the longer the heigth, the slower the falling.
check my thinking.

1. In order to determine which pole reaches the ground first, we need to consider the physical principles involved. The time it takes for an object to fall to the ground depends on its initial height and the acceleration due to gravity. Since both poles are starting from rest, their initial velocities are zero. Additionally, since both poles have the same diameter and mass density, we can assume that their masses are the same.

Now, the key factor is their initial heights. Let's consider the tall pole first. Since it is taller, it has a greater initial height than the short pole. Therefore, it will take longer for the tall pole to fall and reach the ground compared to the short pole. This is because both poles will experience the same acceleration due to gravity, but the tall pole has a greater distance to cover.

In conclusion, the short pole will reach the ground first, since it has a smaller initial height compared to the tall pole.

2. When a non-vertical projectile strikes the ground, the vertical component of its momentum is conserved during the collision.

To understand this, let's first consider the motion of a projectile. A projectile is an object that is launched into the air and moves under the influence of gravity. The only force acting on a projectile is gravity, which acts vertically downward. This means that there is no external force acting horizontally on the projectile once it is in the air.

Now, during the motion of a projectile, both its horizontal and vertical components of motion are independent of each other. The horizontal component is constant and unaffected by gravity, while the vertical component is influenced by gravity and follows a parabolic trajectory.

When a projectile strikes the ground, there may be a collision between the projectile and the surface. During this collision, the horizontal component of the projectile's momentum is not conserved, as it may experience forces from the ground that change its direction or bring it to a stop. However, the vertical component of the projectile's momentum is conserved, assuming there are no vertical forces acting on it during the collision.

This conservation of momentum in the vertical direction is due to the absence of any external vertical force acting on the projectile. Therefore, the vertical component of the projectile's momentum remains the same before and after the collision with the ground.