Projectile Motion Problem: Two Physics Students on a Balcony

Physics Problem: Two Balls Thrown from a Balcony

Two physics students are on a balcony 19.6 m above the street. One student throws a ball vertically downward at 14.7 m/s; at the same instant, the other student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down. What is the velocity of each ball as it strikes the ground?

Two balls thrown from a balcony, one upward and one downward at the same speed, will strike the ground with the same velocity (-24.5 m/s) due to the effect of gravity.

Explanation:

The subject of this problem is physics, specifically the topic of kinematics. In this problem, we can use the following kinematic equation that connects initial velocity (Vi), final velocity (Vf), acceleration (a), and displacement (d): Vf² = Vi² + 2*a*d. For the ball thrown downwards, the initial velocity is -14.7 m/s (we take down as negative), acceleration due to gravity is -9.8 m/s², and displacement is -19.6 m (downward from the balcony to the ground).

Substituting these values into the kinematic equation, we find Vf² = (-14.7 m/s)² + 2*(-9.8 m/s²)*(-19.6 m), which gives a final velocity of approximately -24.5 m/s (downwards).

For the ball thrown upwards, the initial velocity is +14.7 m/s, but the rest of the process is the same. Again substituting the known values into the kinematic equation, we find the final velocity to be approximately -24.5 m/s (downwards), the same as the first ball.

In conclusion, despite the different initial directions, both balls strike the ground with the same velocity due to gravity's effect on their motion, demonstrating the symmetry of projectile motion.

Do both balls have the same final velocity when they hit the ground?

Yes, both balls thrown from the balcony, one upward and one downward at the same speed, will strike the ground with the same velocity of approximately -24.5 m/s due to the effect of gravity.