Homework Help: Velocity Question

Essentially these types of problems are asking you the velocity at the instant before the object collides with the ground. Hence, unless there are external forces dissipating the objects energy, its final (at the instant before it touches ground) will equal its initial.

 

I think this is the qoestion on projectile motion. If air resisance is neglected, final velocity is equal to initial velocity. It will never become zero throughout the time of flight. if air resistance is included, final velocity will be less than initial one.

 

The velocities in the picture are not equal, but of equal magnitude, as the directions differ. You can say that the speeds are equal.

If it is a projectile, the horizontal component is constant during the motion as only vertical force -gravity- acts on the object. Energy is conserved, so mgy_i+1/2 mv_i²=mgy_f+1/2 mv_f². If y_i=y_f the square of the velocities are equal, v_i²=v_f². That means equal magnitudes |v_i|=|v_f|, that is, equal speeds.


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