18.
Applications of Parabolar-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 curve 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)=-5t2+40t+1.2
a. What is the degree of the polynomial
ii. 1
iii. 2
iv. 3
b. Find the height of the projectile 4 seconds after it is launched
i. 80.2 m ii. 81.2 m iii. 81.8 m iv. 84 m
c. The polynomial is classified as
on the basis of number of terms.
i. Linear Polynomial ii. Monomial iii. Binomial iv. Trinomial
d. The name of polynomial on the basis of degree is.
i. cubic-polynomial
ii. Constant polynomial
iii. Quadratic polynomial
iv. Bi-quadratic polynomial
e. If equation of parabola is given by p(x)=x2-5x+6, then it's factors are
i. X-3
ii. X-2 iii. both (i) and (ii) iv. None of the above
Answers
Answer:
(1)=2
(2)=81.2
(3)=trinomial
(4)=quadratic
(5)=both a and b.
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Answer:
(a) Degree of the polynomial = 2
(b) The height of the projectile at t = 4 is 81.2m
(c) It will be classified as a trinomial.
(d) It is a quadratic equation.
(e) Both ( x - 3 ) and ( x - 2 ) will be the factors of x² - 5x + 6.
Step-by-step explanation:
Given
p(t) = -5t² + 40t + 1.2
(a) Degree of the polynomial is the highest power amongst all the terms of the polynomial.
Here as t² is the highest power, therefore, degree = 2
(b) Height of the projectile at t = 4
= -5*4² + 40*4 + 1.2
= -80 + 160 + 1.2
= 80 + 1.2
= 81.2m
Therefore, the height of the projectile at t = 4 is 81.2m
(c) As there are three terms in the given polynomial, it will be called a trinomial.
(d) We know that an equation of the form ax² + bx + c = 0 is a quadratic equation.
Here, the equation -5t² + 40t + 1.2 can also be written as ax² + bx + c = 0 with a = -5, b = 40 and c = 1.2
Therefore, it is a quadratic equation.
(e) Given equation is x² - 5x + 6 = 0
By mid-term splitting,
=> x² - 3x - 2x + 6 = 0
=> x(x - 3) -2(x - 3) = 0
=> (x - 3) (x - 2) = 0
Therefore, both ( x - 3 ) and ( x - 2 ) will be the factors of x² - 5x + 6.