Content
Access custom-built, exam-style problems for modelling. Each problem has a full solution and mark-scheme, as well as AI grading and support.
Select a Difficulty:
6 / 39 problems visible - Upgrade to view all problems
!
0 / 5
The gravitational force of the Sun on a planet is proportional to the mass of the planet, and inversely proportional to the square of the distance between the planet and the Sun.
Let F be the gravitational force exerted by the Sun on Earth, which has a mass of 6×1024kg and is 1AU (astronomical unit) from the Sun.
Neptune's mass is approximately 17 times that of Earth, and it is 30AU from the Sun.
Find an expression in terms of F for the gravitational force exerted by the Sun on Neptune.
The force of gravity of the Sun on Jupiter, which is 5.20AU from the Sun, is 12 times that force on Earth.
Calculate the mass of Jupiter.
!
0 / 4
A biker climbs a mountain with a slope of 8%. He bikes a distance of 12km along the road to reach a summit at an altitude of 1675m.
Show that he has climbed 960m.
The relationship between the height h (in meters) of the biker above sea level and the distance d (in kilometers) travelled along the road can be modeled by
Find the values of a and b.
State the significance of the value of b in this context.
!
0 / 6
A radioactive substance has a half-life of 5700 years. This means every 5700 years, the amount of substance is reduced to half of what it was at the beginning.
A sample initially contains 80g of the substance.
Write down how much remains after one half-life and after two half-lives.
After how many years will the amount of substance first fall below 20g?
A bone fragment is found to contain 10% of its original radioactive isotope.
Use the concept of half-lives to estimate its age, giving your answer to the nearest 1000 years.
!
0 / 7
!
0 / 6
0 / 8
Ask Plex AI about problem 4
Get hints, ask questions, and work through this problem step by step