Astudent builds a rocket-propelled cart for a science project. its acceleration is not quite high enough to win a prize, so he uses a larger rocket engine that provides 36% more thrust, although doing so increases the mass of the cart by 11%. by what percentage does the cart's acceleration increase?

This question can be solved by using the formula of thrust.

The cart's acceleration will increase by "22.5 %".

The thrust force of an object is given by the following formula, as stated in Newton's Second Law of Motion:

F = ma

where,

F = thrust

m = mass

a = acceleration

------------- eqn (1)

Now, an increase of 36 % in thrust means F becomes 1.36 times (1 + 0.36) of the original value. While an increase of 11 % in mass means m becomes 1.11 times (1 + 0.11) of its original value.

Therefore,

1.36 F = (1.11 m)a'

using eqn (1):

a' = 1.225 a

Hence, percentage increase in the value of acceleration will be:

Increase = 1.225 - 1 = 0.225

Increase = 22.5 %

Find the attached picture demonstrating thrust force.

Learn more about thrust here:

link

From Newton #2 . . . F = M A

We'll be looking for acceleration, so before we start, let's divide each side of Newton #2 by (mass) :  A = F / M .  

Original acceleration = F / M

New acceleration = (1.36 F) / (1.11 M)

New acceleration = (1.36 / 1.11) (F / M)

New acceleration = (1.23) (F/M)

New acceleration = (1.23) (original acceleration)

Using the bigger rocket engine increases the acceleration by 23% .

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.