Falling Body Problems For the most part, these problems can be solved using the equations on page one of the EQUATIONS page. The trick is to select the right equation; they are not one-size-fits-all. Each equation has four quantities in it, which means you will need to know three quantities to use any equation. It is recommended that, as you read through a problem, you should write down the given information in a table of data. In doing this you must keep like data together. You should keep a separate table of data if any of these conditions are in place: 1) there is more than one object moving--use a separate table for each (see #4 below); 2) the object in motion has more than one acceleration during the event--use a separate table for each acceleration (see problem 7); 3) an ample description of one part of a trip is given, but questions are asked about another part--use a separate table of data for each part (see #6 below). Have fun. 1. A ball is dropped from a cliff 50 m high. a) With what velocity does it hit the ground? B) How long is the ball in the air? Solution 2. A ball is tossed into the air with a velocity of 29.4 m/s. a) Where is it at the end of each of the first six seconds of flight? How fast is it going after each of the first six seconds of flight? 3. A ball is tossed upward at 25 m/s. It is subsequently caught at the same level as that from which it was projected. a) How long was it airborne? To what height did it rise?Solution 3xOne way to solve the local solid waste disposal problem is to drop bags of trash from interstate hiighway overpasses into the cargo bed of pick up trucks owned by non-residents. For a successful event, timing is everything. a) If the overpass is 4m above the truck bed, how long after the bag is released will it hit the bed? b) If the truck is moving at 40 m/s, where is the leading edge of the truck bed when the bag is released? "He who hesitates is lost." c) If the truck bed is 2.5 m long, for how long will the truck bein position to capture the bag? 4. A ball is dropped from some high place. One second later another ball is thrown down with a speed of 15 m/s. a) How far from the start have they traveled when they are side by side? b) At what time does this occur? c) How fast is each ball traveling at that instant? 5. A naughty little boy is dropping water balloons from the roof of a building 20 m tall. His technique is to drop one, wait one second, and the throw another down so that the two balloons hit their target at the same time. a) How long does it take balloon 1 to make the trip? Balloon 2? b) What should be the velocity of the second balloon when it is launched? Solution 6. A ball falls from rest from a height of 4 m and subsequently rebounds to a height of 3 m. The ball is on the floor for .025 s. What acceleration does the ball experience while it is on the floor? 7. A bowling ball falls from rest from a diving board and hits the water one second later with some velocity. It then sinks to the bottom with this same constant velocity, striking the bottom 4 s after hitting the water surface. How deep is the water?Solution 8. The following question regarding elevator safety is often asked. An elevator car is 10 m above the bottom of the shaft when the cable snaps. All redundant safety mechanisms fail. The only hope for passengers is to jump from the floor at the moment of impact. A) What jumping speed makes this caper survivable? B) Is this scenario plausible? 9. Ball #1 is dropped from rest from a height of 30 m. At that same moment, Ball #2 is launched from the ground, rises some distance, and returns to the ground where it arrives simultaneously with Ball #1. a) How long did this event take? b) What was the launch velocity for ball #2? c) To what height did ball #2 rise? d) How fast was each ball moving when it hits the ground?Solution 10. Ball #1 is tossed into the air at 5 m/s. a) To what height does it rise? b) How long does it take to reach this highest point? Ball #2 is launched with the same initial velocity at the moment that Ball #1 is at its highest point. c) where and when do the two balls meet?   Return to falling bodies this page was reviewed 01/23/09.