# Simple what is velocity at time t problem

Simple "what is velocity at time t" problem

## Homework Statement

A helicopter is lifting off. The only forces are air (up) and gravity. What is the vertical speed at time t if it took off at time t=0?

## Homework Equations

g = F(air)/m, g=Δv/Δt

## The Attempt at a Solution

F(air)/m = Δv/Δt

v = tF(air)/m, but I'm told that this is wrong. I believe I need to include g. What am I missing?

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Simon Bridge
Homework Helper

Draw a free-body diagram for the helecopter.
The sum of the forces is mass times acceleration... acceleration of the helecopter is not going to be g.

Andrew Mason
Homework Helper

## Homework Statement

A helicopter is lifting off. The only forces are air (up) and gravity. What is the vertical speed at time t if it took off at time t=0?

## Homework Equations

g = F(air)/m, g=Δv/Δt

## The Attempt at a Solution

F(air)/m = Δv/Δt

v = tF(air)/m, but I'm told that this is wrong. I believe I need to include g. What am I missing?
In order to determine the acceleration you have to add all the forces on the helicopter (ie. by adding the forces as vectors). As Simon points out, the best way to do this is with a vector diagram showing all the forces on the helicopter. Gravity is one of the two forces acting on the helicopter.

How is the net force (vector sum of all forces) related to the motion of the helicopter?

AM

rcgldr
Homework Helper

One missing piece of information is that the upwards force from the air is probably assumed to be constant regardless of the helicopter's vertical speed (not realistic, but probably what the problem statement is assuming).

Yes, I'm pretty sure the F(air) is constant for the purposes of the problem.

So how about this: F(air) + F(weight) = ma + mg where "a" is the upward acceleration of the helicopter. BUt now I have too many variables to solve just for velocity. I have one Δv/Δt for a and one Δv/Δt for g.

What am I STILL missing?

Fnet=Fair-mg
a=Fair/m-g

For constant Fair and g.
v0=0
v(t)=(Fair/m-g)t

Last edited:
Simon Bridge
Homework Helper

Sum of the forces equals mass time acceleration.

Formally:
1. Pick a direction to be positive.
2. Put all the forces in a row with + signs between them (some of the forces will be negative) ... then put an = sign .... then put "ma".
3. then do the algebra.

i.e.
with positive = "upwards"

Fair + (-Fweight) = ma

Notice that Fweight=mg
Put Fair=F (saves typing).

F - mg = ma => a = (F - mg)/m => v(t) = (F - mg)t/m

Notice: do step #2 like that and you'll never mess up the order.

Thank you! I see that I have been over-complicating it.

Simon Bridge