In one day, a 75-kg mountain climber ascends from the 1500-m level on a vertical cliff to the top at 2400 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1350 m. What is her change in gravitational potential energy (a) on the first day?

Video transcript

Welcome back. Everyone in this problem, an adventure with a mass of 70 kg climbs from a valley at an elevation of one multiplied by 10 to the third meters to reach the top of a cliff at an altitude of 2.6 multiplied by 10 to the third meters. Calculate her change in gravitational potential energy in doing so. A says it's 8.8 multiplied by 10 to the fifth jewels. B 9.1 multiplied by 10 to the fifth jewels. C 1.1 multiplied by 10 to the sixth jewels and D 1.3 multiplied by 10 to the sixth jewels. Now we're trying to find a change in gravitational potential energy. What do we know about gravitational potential energy? Well, recall, OK, that, that energy is equal to the mass multiplied by the acceleration due to gravity. G multiplied by the height. OK. So if we are looking for a change in gravitational potential energy, we want delta U which is going to be equal to M it's the same mass. The mass doesn't change here multiplied by G A constant. That doesn't change multiplied by delta H because our height changes in this problem. No. How does our height change? Well, our problem tells us our climber goes from one multiplied by 10 to the third meters to 2.6 multiplied by 10 to the third meters. That's our change in height that we will be able to substitute in this formula and thus solve for the change in gravitational potential energy. So let's go ahead and do that. So our climber has a mass of 70 kg. Let's take the acceleration due to gravity to be 9.8 m per second squared. And now our change in height is going to be the difference between 2.6 multiplied by 10 to the third meters and one multiplied by 10 to the third meters. No, 2.6 minus one. It's gonna be 1.6. So our change in height is 1.6 multiplied by 10 to the third meters. And no, if we go ahead and follow through on our solution here for a change in gravitational potential energy, then we should get it to be equal to one. Sorry, that's 1,097,600 Jews. If we write that to two significant figures, then it's approximately 1.1 multiplied by 10 to the sixth jewels. Thus, this is the change in gravitational potential energy. That means C is the correct answer. Thanks for watching everyone. I hope this video helped.