standing on the ground, you throw a 0.55 kg lunch bag at a friend, you manage to throw the bag straight up (vertically) using 50 J of energy to throw it there is also a crosswind of 0.5 m/s. How high will the bag travel before all of its kinetic energy is converted into gravitational potential energy?

Question

standing on the ground, you throw a 0.55 kg lunch bag at a friend, you manage to throw the bag straight up (vertically) using 50 J of energy to throw it there is also a crosswind of 0.5 m/s. How high will the bag travel before all of its kinetic energy is converted into gravitational potential energy?

Answer 1

KE=PE

KE=mgh

h=KE/mg =50/0.55•9.8 =9.28 m

Answer 2

To find the height at which the bag will reach before all of its kinetic energy is converted into gravitational potential energy, we need to use the principles of conservation of energy.

First, let's break down the problem and analyze the different forms of energy involved. The initial energy is purely kinetic, consisting of both translational and rotational energy due to the crosswind. We'll assume that the rotational energy is negligible for simplicity.

The total energy of the system (kinetic energy + gravitational potential energy) is conserved throughout the motion. As the bag reaches its maximum height, all of its kinetic energy is converted into gravitational potential energy.

The kinetic energy (KE) of an object is given by the equation:
KE = 0.5 * mass * velocity^2

In this case, the kinetic energy used to throw the bag vertically is 50 J. The mass of the bag is 0.55 kg. The initial velocity of the bag is not given, but we can calculate it using the given information of a crosswind.

The crosswind has a velocity of 0.5 m/s. Since the bag is thrown straight up, the crosswind does not affect the initial velocity in the vertical direction. Therefore, the initial vertical velocity (v) will be calculated without considering the crosswind.

Using the equation for kinetic energy, we can rearrange it to solve for velocity:
velocity = sqrt(2 * KE / mass)

Substituting the given values:
velocity = sqrt(2 * 50 J / 0.55 kg)
velocity ≈ 10.105 m/s

Now that we know the initial vertical velocity, we can calculate the maximum height (h) using the conservation of energy principle.

At the highest point, all of the initial kinetic energy will be converted into gravitational potential energy (PE):
PE = mass * acceleration due to gravity * height

Since all the kinetic energy has been converted to potential energy, we can equate these two expressions:
0.5 * mass * velocity^2 = mass * acceleration due to gravity * height

Canceling the mass on both sides of the equation:
0.5 * velocity^2 = acceleration due to gravity * height

Rearranging the equation to solve for height:
height = (0.5 * velocity^2) / (acceleration due to gravity)

Substituting the values:
height = (0.5 * (10.105 m/s)^2) / (9.8 m/s^2)
height ≈ 5.208 meters

Therefore, the bag will travel approximately 5.208 meters high before all of its kinetic energy is converted into gravitational potential energy, assuming no other forces act on it.