Question

Case study: Applications 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 is represented by a polynomial. If the polynomial to represent the distance covered is
p(t) = -57 + 4t + 1.2
i) What is the degree of the polynomial?
0
b) 1
c) 2
d) 3
ii) Find the height of projectile 4 seconds after it is launched.
a) 80.2 m
b) 81.2 m
c) 81.8 m
d) 84 m
ii) The polynomial is classified as
on the basis of number of terms.
a) Linear polynomial b) monomial
c) binomial
d) trinomial
iv) The name of polynomial on the basis of degree is
a) cubic polynomial
constant polynomial
c) Quadratic polynomial
d) Bi-quadratic polynomial
w) If equation of parabola is given by, p(x) = x2 – 5x + 6, then its factors are
a) x-3
c) both a & b
d) None of the above
209​

Answer 1

• 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,

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

Polynomial:

• A polynomial is a mathematical statement made up of variables and constants that can be combined with the use of mathematical operations such as addition, subtraction, multiplication, and whole number exponentiation.

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with non-zero 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.

Here the given polynomial is:

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

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.

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

Putting t = 4 we get

$p(4)=-5 \times 4^{2}+40 \times 4+1.2\\=-80+160+1.2\\=81.2$

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.

Learn more about polynomial here,

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