MYTUTOR SUBJECT ANSWERS

472 views

how to find flight time/distance and greatest hight of projectiles?

is acceleration, v is velocity, is position

vertically:

a = - g

v = u - gt (by integrating with respect to t and setting initial speed u as constant of integration)

s = ut -gt2/2 + s0 (by integrating again and setting initial position s0 as constant of integration, although object if usually projected from origin so s= 0)

horizontally:

a = 0

v = u (constant velocity as acceleration is zero)

s = ut + s0 (again s0 usually 0)

so for an object projected from the origin at speed u at an angle θ from the horizontal, the initial speed in the x direction is ucos(θ) and usin(θ) in the y direction

thus sx = utcos(θ) and sy = utsin(θ) - gt2/2

flight time: this is the value of t when sy returns to zero

0 = utsin(θ) - gt2/2

so either t = 0 (at launch) or usin(θ) - gt/2 = 0

=> flight time is t = 2usin(θ)/g

flight distance: this is the value of sx when sy = 0

when sy = 0, t = 2usin(θ)/g 

so sx = utcos(θ) = 2u2sin(θ)cos(θ)/g = u2sin(2θ)/g (as sin(2θ) = 2sin(θ)cos(θ))

=> flight distance is x = u2sin(2θ)/g

greatest hight:

this is when sy is at a stationary point, ie. when dsy/dt = 0. This is also when vy = 0.

vy = usin(θ) - gt = 0

=> t = usin(θ)/g

=> sy = utsin(θ) - gt2/2 = u2sin2(θ)/g -  u2sin2(θ)/2g =  u2sin2(θ)/2g

=> greatest height is h = u2sin2(θ)/2g


:)

Ben J. A Level Maths tutor, A Level Further Mathematics  tutor

2 years ago

Answered by Ben, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

298 SUBJECT SPECIALISTS

£20 /hr

Alex J.

Degree: Mathematics (Bachelors) - Newcastle University

Subjects offered:Maths

Maths

“About Myself: As a second year student of Mathematics at Newcastle University, I am all too aware of how difficult maths and other sciences can be to engage with, and so it is my aim to make the subjects that I love just as fascinating...”

MyTutor guarantee

£20 /hr

Noam T.

Degree: Mathematics with Mathematical Physics (Bachelors) - University College London University

Subjects offered:Maths, Physics

Maths
Physics

“About Myself: I am an undergraduate student at UCL studying Mathematics with Mathematical Physics. Hoping to go into research after my degree, I have a true passion for my subjects and my aim is to pass on that passion to students in ...”

£30 /hr

Jamie S.

Degree: Economics and Management (Bachelors) - Bristol University

Subjects offered:Maths, Economics

Maths
Economics

“I am a final year student at the University of Bristol, studying Economics and Management and am currently on track to achieve a 1st. I achieved an A* in Economics and an A in Maths A-levels as well as an A* at maths GCSE so would be ...”

About the author

£24 /hr

Ben J.

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Friendly tutor with perfect academic record happy to help you enjoy Maths and get the grades you need! :)”

You may also like...

Posts by Ben

how to find flight time/distance and greatest hight of projectiles?

What's the deal with Integration by Parts?

Other A Level Maths questions

Given that f(x) = (x^2 + 3)(5 - x), find f'(x).

How and when do you use integration by parts?

What is exactly differentiation?

How to prove that (from i=0 to n)Σi^2= (n/6)(n+1)(2n+1), by induction.

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok