Movement in one and two dimensions, where finding Force in a problem

[Vinhster]

Homework Statement

Hello everyone, i have been stuck on this question on the Physics year 12 Nelsons textbook, and it is pissing me off because I've been working so hard on it and i can not get it.
It is in the chapter of Movement in one and two dimensions.
The question is:
A person pushes a lawnmower of mass 20 kg at a constant speed with a force of 100 N directed along the handle, which is at 35 degrees to the horizontal.
What force must the person exert on the lawnmower in order to give it a velocity of 2.0 m/s in 2.5 s?
Most appreciated for the help everyone thank you.

Homework Equations

I think it's relevant to Tcos(theta) = ma > 0

The Attempt at a Solution

I drew a diagram and labeled all the units.
Where:
t = 2.5
v = 2
u = 0
So i used the formula : v = u + at
where i concluded with 2 = 0 + a2.5
a = 2/2.5
a = 0.8 m/s^2
and then i subbed it into the equation
F = ma
where i concluded with F = (20)(0.8)
= 16 N
But the answer in the back of the book says it's 120N =/

 

[PhysDrew]

Well for starters if initially the lawn mower is pushed with a force of 100 N, and the velocity is constant (ie no acceleration), then to accelerate the lawn mower, a force greater than 100 N is required. So modify the force required to accelerate it (remember the angle) and add it to the 100N.

 

[gneill]

Draw a diagram of all the forces acting on the lawnmower. First draw the initial case, where the lawnmower is traveling at constant speed. Since a force is applied to the handle, yet it's moving at constant speed, what's keeping it from accelerating?

Does adding additional force to the handle increase, decrease, or keep this retarding force the same?