MatLAB Answers

1.    The manager of a supermarket collected the data of 25 customers on a certain date. Out of them 5 purchased Biscuits, 10 purchased Milk, 8 purchased Fruits, 6 purchased both Milk and Fruits.

Let B represents the randomly selected customer purchased Biscuits, M represents the randomly selected customer purchased Milk and F represents the randomly selected customer purchased Fruits.

Represent the given information in a Venn diagram. Use that Venn diagram to answer the following questions.

a)       Find the probability that a randomly selected customer either purchased Biscuits or Milk.

b)      Show that the events “The randomly selected customer purchased Milk” and “The randomly selected customer purchased Fruits” are independent.

A ball is thrown vertically upwards with an initial velocity of 30 m/s.

Using a time step of 0.02 s up to 6.20 s, write a matlab code to give a plot of the vertical distance versus

time for this ball.

Hint ; Motion under gravity is described by the equation : 𝑣𝑦 = 𝑣𝑜𝑦𝑡 +1/2𝑔𝑡^2

and gravitational acceleration 𝑔 is here taken as negative.

Then use your code to answer the following questions:

(i) To what maximum height does the ball rise?

(ii) What is the index of time at maximum height?

(iii) How long does it take the ball to ascend to maximum height?

(iv) How long does it take the ball to hit the ground?

(v) What happens to the ball if the sign for gravitational acceleration is taken as positive?

A ball is thrown vertically upwards with an initial velocity of 30 m/s.

Using a time step of 0.02 s up to 6.20 s, write a matlab code to give a plot of the vertical distance versus

time for this ball.

Hint ; Motion under gravity is described by the equation : 𝑣𝑦 = 𝑣𝑜𝑦𝑡 +

1

2

𝑔𝑡

2

and gravitational acceleration 𝑔 is here taken as negative.

Then use your code to answer the following questions:

(i) To what maximum height does the ball rise?

(ii) What is the index of time at maximum height?

(iii) How long does it take the ball to ascend to maximum height?

(iv) How long does it take the ball to hit the ground?

(v) What happens to the ball if the sign for gravitational acceleration is taken as positive?

A company manufactures three products: Engines, Pumps and Fans. They give a discount

of 10% on order for engines if the order is for Rs.5,000 or more. The same discount of

10% is given on pump orders of values of Rs.2,000 or more and on fan orders for

Rs.1,000 or more. On all other orders they do not give any discount.

ball is thrown vertically upwards with an initial velocity of 30 m/s.

Using a time step of 0.02 s up to 6.20 s, write a matlab code to give a plot of the vertical distance versus

time for this ball.

Hint ; Motion under gravity is described by the equation : 𝑣𝑦 = 𝑣𝑜𝑦𝑡 +

1

2

𝑔𝑡

2

and gravitational acceleration 𝑔 is here taken as negative.

Then use your code to answer the following questions:

(i) To what maximum height does the ball rise?

(ii) What is the index of time at maximum height?

(iii) How long does it take the ball to ascend to maximum height?

(iv) How long does it take the ball to hit the ground?

(v) What happens to the ball if the sign for gravitational acceleration is taken as positive?

A rain drop of mass 3gm starts to fall from rest under the effect of gravity from a height of

100m. There is an air drag acting on the rain drop, the drag force is given by the equation,

Fd = bv.

Here, b = a × 10^-3kgs^-1s

a = 2

(a) Determine the governing differential of the system.

(b) Build a SIMULINK model of the system using transfer functions.

(c) Show velocity vs time graph with and without the effect of air drag on the same

plot.

(d) Show height vs time graph with and without the effect of air drag on the same

plot.

(e) From your graphs, determine the approximate time required for the rain drop to

reach the ground.