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% .