The rubber ball falls 490 meters in 10 seconds, 1960 meters in 20 seconds, and an object dropped from a window takes approximately 4 seconds to fall 78.4 meters. The final velocity of the ball is 98 m/s, with an average velocity of 49 m/s. The box of supplies from an airplane reaches the ground in approximately 80 seconds with a final velocity of 784 m/s.
1 - To determine how far a rubber ball will fall in 10 seconds, we can use the formula for free fall:
Distance (d) = 1/2 * 9.8 m/s^2 * (10 s)^2
Distance (d) = 490 meters
2 - To find the distance fallen in 20 seconds, we can use the same formula with t = 20 s:
Distance (d) = 1/2 * 9.8 m/s^2 * (20 s)^2
Distance (d) = 1960 meters
3 - To determine the time it takes for an object to fall a distance of 78.4 meters, we can rearrange the formula and solve for time:
d = 1/2 * g * t^2
t = sqrt(2d/g)
t ≈ sqrt(2 * 78.4 / 9.8)
t ≈ 4 seconds
4 - To calculate the final velocity of the ball in Problem 1, we can use the formula:
Final Velocity (v_f) = g * t
Final Velocity (v_f) = 9.8 m/s^2 * 10 s
Final Velocity (v_f) = 98 m/s
5 - The average velocity of the ball in Problem 1 can be found by dividing the total distance fallen by the time taken:
Average Velocity = Total Distance / Time
Average Velocity = 490 m / 10 s
Average Velocity = 49 m/s
6 - To determine how long it will take for the box of supplies to reach the ground when dropped from an airplane at an altitude of 31,360 meters, we can use the same formula:
t = sqrt(2d/g)
t ≈ sqrt(2 * 31,360 / 9.8)
t ≈ 80 seconds
7 - To find the velocity of the box when it hits the ground, we can use the formula:
Final Velocity (v_f) = g * t
Final Velocity (v_f) = 9.8 m/s^2 * 80 s
Final Velocity (v_f) = 784 m/s