1. Notes on Motion VI Free Fall A Special type of uniform acceleration

2. Free Fall When an object is only allowed to move under the influence of gravity. When you drop a ball, it is in free fall! When you throw a ball downward, it is in free fall! (After it is released) When you throw a ball upward, it is in free fall! (After it is released)

3. Free Fall When an object is in free fall, it has a uniform acceleration. Objects in free fall are ALWAYS accelerated downward by gravity. On Earth, objects in free fall are accelerated downward at a rate of 9.8 m/s/s (or 9.8 m/s 2 ). When we are working with formulas we use “g” to represent the acceleration due to gravity. g = 9.8 m/s 2 In the English System of measurement g = 32 ft/s 2.

4. Free Fall Speed/Velocity In general, the formula we use to find the velocity of an object in free fall is: The acceleration of an object in free fall is the acceleration due to gravity, g, and is downward so a = -g = -9.8-m/s/s. Rewriting to find time, you get: The speed of an object in free fall is just the velocity without the sign.

5. Example Problem 1 A cliff diver dives from the top of a cliff. If he is able to fall for 10-s, what will his speed be when he hits the water? Useful Formulas Know Find Formula Solution v i = 0-m/s t = 10-s Free Fall v f = ? Since we are only asked for speed, we can ignore the (-), so the speed is 98-m/s.

6. Example Problem 2 A ball is thrown upward into the air at 35-m/s. How long will it take the ball to reach its maximum height? Useful Formulas Know Find Formula Solution v f = 0-m/s v i = 35-s Free Fall t = ? What would the hang time of this ball be? Since it takes 3.6-s to reach its maximum height, it will take an additional 3.6-s to reach the ground again. 3.6 + 3.6 = 7.2-s

7. Distance in Free Fall When an object that started from rest had a uniform acceleration, we had an equation for the distance it travelled in a given time: But since we know the acceleration of the object is “g” (9.8-m/s 2 ), we can change this to: If we need to find the time it takes an object to fall a certain distance, we can solve this equation for t:

8. Example Problem 3 A rock is dropped from the top of the Empire State Building in New York City. The height of this building is 381-m. How far will this rock have fallen in 5-s? Useful Formulas Know Find Formula Solution t = 5-s Free Fall d = ? How far from the ground will the rock be at this time? h = 381 - 122.5 = 258.5-m

9. Example Problem 4 A rock is dropped from the top of the Empire State Building in New York City. The height of this building is 381-m. How long will it take for the rock to hit the ground? Useful Formulas Know Find Formula Solution d = 381-m Free Fall t = ?

10. Example Problem 5 A rock is dropped from the top of the Empire State Building in New York City. The height of this building is 381-m. How fast will the rock be travelling just as it hits the ground? Useful Formulas Know Find Formula Solution t = 8.8-s From Example 4 Free Fall v f = ? Since we are only asked for speed, we can ignore the (-), so the speed is 86.2-m/s. FYI: 86.2-m/s is approximately 194-mph. That could do some damage.

11. Finding Maximum Height When an object is thrown upward, we know that the time it takes for it to reach its maximum height is the same as the time for it to fall back to the ground from that height. We can use this information to help us find the maximum height of the object. First Find the time it takes to reach its maximum height using the formula: Second Use the time found in the first step to calculate the distance it falls from its maximum height. Use: We also know that its velocity at its maximum height is 0.

12. Example Problem 6 A rifle fires a bullet at 896-m/s. If the bullet is fired straight up, find its maximum height. Useful Formulas Know Find Formula Solution v i = 896-m/s vf = 0-m/s Free Fall t = ? First find the time to maximum height: NOW USE THIS TIME TO FIND THE MAXIMUM HEIGHT

13. Example Problem 6 Continued A rifle fires a bullet at 896-m/s. If the bullet is fired straight up, find its maximum height. Useful Formulas Know Find Formula Solution t = 91-s Free Fall d = ?