Final answer:
To calculate the height of the bounce, use the formula Vf = Vi + gt to find the change in velocity during the bounce. Then use the kinematic equation Vf^2 = Vi^2 + 2aΔx to solve for the height of the bounce.
Step-by-step explanation:
To calculate the height of the bounce, we need to first calculate the change in velocity during the bounce. We know that the surface gravity on P67/Churyumov-Gerasimenko is 10^-6 times that of Earth. Given that the Philae lander touched down again 1 hour and 53 minutes later, we can calculate the change in velocity using the formula Vf = Vi + gt, where Vf is the final velocity, Vi is the initial velocity, g is the acceleration due to gravity, and t is the time interval.
Since the initial velocity of the lander is unknown, we can assume it is zero. Therefore, the final velocity of the lander when it touched down again is equal to gt. We can calculate the acceleration due to gravity on P67/Churyumov-Gerasimenko by multiplying the acceleration due to gravity on Earth (9.8 m/s^2) by 10^-6. Once we have the value for g, we can plug it into the formula.
Once we have the change in velocity, we can use the kinematic equation Vf^2 = Vi^2 + 2aΔx, where Vi is the initial velocity, a is the acceleration due to gravity, and Δx is the change in position. Since the lander started and ended at the same position, Δx is equal to twice the maximum height of the bounce. Rearranging the equation, we can solve for Δx and divide it by 2 to get the height of the bounce.