Theory question about a ball projected vertically against air resistance?

Question

is it possible for a ball that is projected upwards vertically against air resistance to reach a max height of approx 18m in 25 seconds? what it is ive done a calculation about a ball travelling upwards against air resistance using a quadratic air resistance model and it reaches a max height of approx 18m, i have found t and it is aprrox 25 seconds (this is all happening on earth with 9.81 ms^-2) i was just wondering have i done the calcualtion wrong or could a ball travel that slow upwards to its max height against air resistance? (its taking approx over a second to travel per metre approx 1.4 s) can this be correct any help thanks

Answer 1

There are so many variables which you have not mentioned and it makes it difficult to comment. E.g. what is the size and mass of the ball, the initial acceleration, the temperature of the air would also affect the drag, the type of surface on the ball too, spin imparted, etc. This is an fluid dynamics question and can only be solved if we know the different conditions. Your figures do not sound right though.

Answer 2

Air resistance is going to make very little difference. To reach a maximum height of 18m the initial velocity will be about 19m/s and it will take about 2 seconds to reach this height.

Whatever the correct answer is when air resistance is included cannot be much different to these figures.

Answer 3

well v = d/t and on a striahgt upwards projection the ball would have to travel at 15 m/s constantly.. this is assuming no acceleration, and we just want to see if 0.72 m/s is possible.

i do know for a fact that a table tennis ball can go around 9 m/s.. so .72 is much less so it should be possible.

Answer 4

It looks very wrong, Ill take a stab and say its initial velocity must have been at least 245m/s for it to be in the air that long( not including friction) seen as gravity is acting on it at -9.81m/s. decelerating from 245m/s to 0m/s in 25 seconds would mean it would reach a higher maximum height, so I do not believe its possible.

I'm probably completely off the mark.