You throw a ball upward with an initial speed of 10 m/s. Assuming that there is no air resistance, what is its speed when it returns to you?
10 m/s, same as it was when it started.
To find the speed of the ball when it returns to you, we can use the concept of conservation of energy. Since there is no air resistance, the total mechanical energy of the ball remains constant throughout its motion.
At the initial point when you throw the ball upward, it has a certain amount of kinetic energy due to its initial speed and a certain amount of potential energy due to its height from the ground.
As the ball rises against gravity, its kinetic energy decreases and is converted into potential energy. At the highest point of its trajectory, the ball momentarily stops and then starts falling back down.
When the ball returns to you, it reaches the same height from which it was initially thrown. At this point, all the potential energy is converted back into kinetic energy.
Since the total mechanical energy is conserved, we can equate the initial kinetic energy to the final kinetic energy.
Initial Kinetic Energy = Final Kinetic Energy
The initial kinetic energy can be calculated using the formula:
Kinetic Energy = 1/2 * mass * velocity^2
Given that the initial speed of the ball is 10 m/s, we can substitute this value into the formula:
Kinetic Energy = 1/2 * mass * (10)^2
To get the final kinetic energy, we use the same formula but with the final speed of the ball as the variable:
Kinetic Energy = 1/2 * mass * (final velocity)^2
Setting the initial and final kinetic energies equal to each other:
1/2 * mass * (10)^2 = 1/2 * mass * (final velocity)^2
Since mass is common to both sides of the equation, we can cancel it out:
(10)^2 = (final velocity)^2
Simplifying further:
100 = (final velocity)^2
Taking the square root of both sides:
final velocity = √100
final velocity = 10 m/s
Therefore, the speed of the ball when it returns to you is 10 m/s.