Calculate the Final Velocity of a Ball Thrown From a Balcony
What is the magnitude of the velocity of the first ball as it strikes the ground?
Two students are on a balcony 21.9 m above the street. One student throws a ball vertically downward at 13.6 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.
Answer:
The magnitude of the velocity of the first ball as it strikes the ground is 24.77 m/s.
To calculate the final velocity of the first ball when it strikes the ground, we need to consider the initial velocity, gravity, and the total distance the ball travels.
Given:
Initial Velocity (Vo) = 13.6 m/s
Gravity (g) = 9.8 m/s2
Total distance = 21.9m
The final velocity of the ball can be calculated using the formula:
Vf = Vo + g*t
However, we need to find the time (t) it takes for the ball to reach the ground. This can be done by using the equation of motion:
D = Vo * t + (0.5 * g * t2)
By substituting the values, we get:
21.9 = 13.6 * t + 4.9 * t2
Solving the quadratic equation, we find the value for time (t) to be t = 1.14 seconds.
Substitute the time back into the formula for final velocity:
Vf = 13.6 + 9.8 * 1.14 = 24.77 m/s
Therefore, the magnitude of the velocity of the first ball as it strikes the ground is 24.77 m/s.