A projectile is a type of motion in which an object follows a parabolic path, also known as its trajectory which is represented by a polynomial. The range, height and time of the flight that the object will experience while in projectile motion are determined by the angle at which it is launched.A ball is thrown upwards at a certain angle with the horizontal and it returns to the ground describing a parabolic path. The polynomial to represent the distance covered by the ball is noted to be p(t) = –2t 2 + 20t + 1.4, where t is the time taken to cover the distance.
Based on the given information, answer the following questions:
(a) Find the degree of the given polynomial p(t).
(b) What is the distance covered by the ball, 2s after it is thrown?
(c) What is the name of the polynomial on the basis of its degree?
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Answer:
(a) Degree = 2
(b) Distance covered in 2 seconds = 33.4 meters
(c) Quadratic Polynomial
Step-by-step explanation:
(a) Degree of a polynomial is the highest exponent of "x" in the polynomial.
(b) Distance covered by the ball is a function of time, given by the function:
p(t) = -2t²+ 20t + 1.4
Replacing "t" with "2":
=> p(2) = -2(2)² + 20(2) + 1.4
=> p(2) = -8 + 40 + 1.4
=> p(2) = 33.4 m
(c) Polynomials with degree 2 are called Quadratic Polynomials.
Example:
• ax² + bx + c
• x²+ 1
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