I NEED URGENT HELP!!
Bob is riding his bike along at 2m/s and drops his 2kg backpack from a height of 1.5 meters. What is the backpacks resulting velocity when it strikes the ground?
To find the backpack's resulting velocity when it strikes the ground, we can use the law of conservation of mechanical energy. The law states that the total mechanical energy (kinetic energy + potential energy) of an object remains constant if no external forces (like air resistance) are acting on it.
In this case, we have gravitational potential energy converting into kinetic energy. The gravitational potential energy formula is given by:
Potential Energy = mass * g * height,
where mass is the mass of the object (2 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and height is the height from which the backpack was dropped (1.5 m).
So, the potential energy of the backpack can be calculated as follows:
Potential Energy = 2 kg * 9.8 m/s^2 * 1.5 m,
Potential Energy = 29.4 Joules.
Since no external forces are acting on the backpack, the potential energy is converted entirely into kinetic energy as it falls to the ground. The formula for kinetic energy is:
Kinetic Energy = 0.5 * mass * velocity^2.
We can rearrange this formula to solve for velocity:
velocity^2 = (2 * Potential Energy) / mass,
velocity^2 = (2 * 29.4 J) / 2 kg,
velocity^2 = 29.4 m^2/s^2,
velocity ≈ 5.42 m/s.
Therefore, the backpack's resulting velocity when it strikes the ground is approximately 5.42 m/s.