Derive an expression for the time taken, (t) for a test mass to fall to the ground from a height (h) in a uniform gravitational field (g = 9.81 ms^-2)

We first build an intuition for exactly what acceleration is and what we expect to happen. In the uniform gravitational field approximation, we assume h to be much less than the radius of the Earth. Therefore, the higher we drop the test mass from, the larger the velocity of the test mass when it hits the ground at h = 0. Derivation: We take velocity = dh/dt = acceleration(g)*time(t), and then use the required calculus to integrate to find the expression: h = (1/2)gt^2 . We finally tidy this up by rearranging using basic algebra to express t as a function of h t(h) = SQRT(2h/g) (I would then very likely ask to plot that function so that the intuitions developed at the start can be solidified and we can gain some confidence in the use of calculus to solve real problems.) 

Answered by Charlie B. Physics tutor

1677 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Give examples of how the photoelectric effect supports the particle nature of light and defies the wave theory.


If you have 1.33g of oxygen (Mr = 32) in a container of volume 1000cm^3 at atmospheric pressure (101.3*10^3 Pa), what is the temperature of the gas in Celsius? R=8.314


A sample of pure gold has a density of 19300 kgm^-3. If the density of a gold nucleus is 1.47x10^17Kgm^-3, discuss what this implies about the structure of the gold atom. [4 marks]


An electron is emitted from a cathode in an electron gun, with a potential difference of 150kV. Find the velocity of the electron after it is accelerated and find the De Broglie wavelength.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences