A bungee jumper has a mass of 67 kg.The total height of the jump towards Earth is 210 m.Calculate the speed of the bungee jumper at the bottom of the jump just before the bungee cord stretches and catches them.Gravitational field strength = 9.8 N/kgIgnore the effects of air resistance.Give your answer to three significant figures.
Question
A bungee jumper has a mass of 67 kg.The total height of the jump towards Earth is 210 m.Calculate the speed of the bungee jumper at the bottom of the jump just before the bungee cord stretches and catches them.Gravitational field strength = 9.8 N/kgIgnore the effects of air resistance.Give your answer to three significant figures.
Solution
To solve this problem, we can use the principle of conservation of energy. This principle states that the total energy in a closed system remains constant. In this case, the bungee jumper's potential energy at the top of the jump is converted into kinetic energy at the bottom of the jump.
Step 1: Calculate the potential energy at the top of the jump. Potential energy (PE) is given by the formula PE = mgh, where m is mass, g is gravitational field strength, and h is height.
PE = 67 kg * 9.8 N/kg * 210 m = 138282 Joules
Step 2: At the bottom of the jump, all this potential energy has been converted into kinetic energy. Kinetic energy (KE) is given by the formula KE = 1/2 mv^2, where m is mass and v is velocity.
Setting PE equal to KE gives us:
138282 Joules = 1/2 * 67 kg * v^2
Step 3: Solve for v.
v^2 = 2 * 138282 Joules / 67 kg = 4124.72
v = sqrt(4124.72) = 64.22 m/s
So, the speed of the bungee jumper at the bottom of the jump, just before the bungee cord stretches and catches them, is approximately 64.2 m/s to three significant figures.
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