Projectile Mothion (1 Viewer)

[LeetSpeek]

Determine the maximum height and range of a 50 kg artillery shell fired at a velocity of 200 ms<SUP>-1</SUP> from a gun 200 metres above sea level.

Are the answers

height - 3061.22 m
range - 4180.44 m

thanks

 

[shady145]

you need an angle

 

[Dx_God]

you need an angle

not really, since he stated MAX height and MAX range (meaning angle=90 and 45 degrees respectively)



as for u op, i don't think the height is 3061...m. i got 2238.735984m from letting the angle being 90 degrees and finding out t=20.38...s and subbing it into the y-function (also i assumed g to be 9.81m/(s^2)). for range i got 5112...m. i can't be bothered explaining the process right now but u can ask me how i got it later if ur interested. (Note: i used math ex1 knowledge to solve the question)

 

[k02033]

not really, since he stated MAX height and MAX range (meaning angle=90 and 45 degrees respectively)

using 45 degrees to get the maximum range is only true if the landing position is at the same altitude as the launch position, so using 45 degrees will not always yield the max range in all situations. ie when projectile is fired from a cliff.

lets assume an axis where the base of the cliff is the origin,



this is the range formula for a projectile landing at the same altitude, maximise it using calculus will give you 45 degrees, telling you to launch at 45 degrees to get max range..

but this is the range formula in general



where d is height of the cliff, and maximising this is harder, requiring chain rule and product rule

being lazy and using a math package,

i got 4195 as the range.. and 43 degrees launch angle

 

[LeetSpeek]

I thought that you needed a situation to get the maximum range and maximum height simulatenously so i assumed 45 degrees.