Gandalf's fireworks
Gandalf shoots off fireworks at Bilbo's birthday party. The fireworks go off at 100 m/s from the ground. They go up, explode, and then come back down immediately. The moment the fireworks shoot up, Bilbo rushes to his house 50 meters away at a rate of 5 m/s. He takes 1 second to grab the ring and rushes back at a rate of 8 m/s. How long before Gandalf's fireworks come to the ground will Bilbo return to the party with the ring?
Express your answer in seconds as a decimal to the nearest hundredth.
The acceleration of gravity is -9.8 m/s^2. Neglect air resistance.
The answer is 3.16.
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1 solution
The fireworks start at a speed of 100m/s, losing 9.8 m/s per second due to gravity. This means the fireworks will go up for 100/9.8 ≈ 10.204 seconds. We multiply this by 2 to get the total time, ending with about 20.41 seconds. Bilbo takes 50/5=10 seconds to get to his house, 1 second to get the ring, and 50/8=6.25 seconds to get back. Adding this up we get 17.25. 20.41-17.25=3.16, which is the answer.