A10-kg projectile is fired straight up with an initial velocity of 500 m/s. (a) what is the projectile’s potential energy at the top of its trajectory? (b) what would be the maximum potential energy if the projectile were fired at a 450 angle rather than straight up?

(a) the initial kinetic energy of the projectile is equal to:

The projectile is fired straight up, so at the top of its trajectory, its velocity is zero; this means that it has no kinetic energy left, so for the law of conservation of energy, all its energy has converted into potential energy, which is equal to


b) If the projectile is fired with an angle of , its velocity has 2 components, one in the x-direction and one in the y-direction:



This means that at the top of its trajectory, only the vertical velocity will be zero (because the horizontal velocity is constant, since the motion on the x-axis is a uniform motion). Therefore, at the top of the trajectory, the projectile will have some kinetic energy left:

For the conservation of energy, the initial energy mechanical energy must be equal to the mechanical energy at the highest point:

the initial kinetic energy is the same as point a), so we can re-arrange this equation to find the new potential energy at the top of the trajectory:

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.