Question

Application of Parabolas Projectile motion: An object which is thrown or projected into the air, subject to only the acceleration of gravity is called a projectile, and its path is called its trajectory. This curved path was shown by Galileo to be a parabola. Parabola represented by a polynomial. If the polynomial to represent the distance covered is, p(t)=-5t^2+40t+1.2

What is the degree of the polynomial?

Find the height of the projectile 4 seconds after it is launched.

The polynomial is classified as …………. on the basis of number of terms.

The name of polynomial on the basis of degree is……………….​

Answer 1

SOLUTION

GIVEN

Application of Parabolas Projectile motion: An object which is thrown or projected into the air, subject to only the acceleration of gravity is called a projectile, and its path is called its trajectory. This curved path was shown by Galileo to be a parabola. Parabola represented by a polynomial. If the polynomial to represent the distance covered is,

$\sf{p(t) = - 5 {t}^{2} + 40t + 1.2 }$

TO DETERMINE

1. What is the degree of the polynomial?

2. Find the height of the projectile 4 seconds after it is launched.

3. The polynomial is classified as … on the basis of number of terms.

4. The name of polynomial on the basis of degree is…

CONCEPT TO BE IMPLEMENTED

Polynomial

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

Monomial : A monomial is an expression in algebra that contains one term

Binomial : In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial.

Trinomial : A trinomial is a polynomial consisting of three terms or monomials.

EVALUATION

Here the given polynomial is

$\sf{p(t) = - 5 {t}^{2} + 40t + 1.2 }$

1. Here the variable is t

Now the highest power of its variable that appears with nonzero coefficient = 2

Hence degree of the polynomial = 2

2. Here the given polynomial is

$\sf{p(t) = - 5 {t}^{2} + 40t + 1.2 }$

Putting t = 4 we get

$\sf{p(4) = - 5 \times {4}^{2} + 40 \times 4+ 1.2 }$

$\sf{ = - 80 +160+ 1.2 }$

$\sf{ = 81.2 }$

The height of the projectile 4 seconds after it is launched = 81.2 unit

3. Since the number of terms in the polynomial is 3

Hence the polynomial is classified as trinomial on the basis of number of terms.

4. Since the degree of the polynomial is 2

Hence the name of polynomial on the basis of degree is quadratic polynomial

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