Question

A coach throws a football from a height of 4 feet with an initial velocity of 59 feet per second at an elevation angle of 45°. Which parametric equations represent the path of the football?Which parametric equations represent the path of the football?

A) x(t) = 59sin(45⁰)t and y(t) = –16t² + 59cos(45⁰)t
B) x(t) = 59cos(45⁰)t and y(t) = –16t² + 59sin(45⁰)t
C) x(t) = 59cos(45⁰)t and y(t) = –16t² + 59sin(45⁰)t + 4
D) x(t) = 59sin(45⁰)t and y(t) = –16t² + 59cos(45⁰)t + 4

Answer 1

The correct parametric equations that represent the path of the football are x(t) = 59cos(45⁰)t and y(t) = -16t² + 59sin(45⁰)t + 4. The horizontal component remains constant, while the vertical component is affected by gravity and the initial vertical velocity.

Step-by-step explanation:

The correct parametric equations that represent the path of the football are:

x(t) = 59cos(45⁰)t

y(t) = -16t² + 59sin(45⁰)t + 4

In these equations, x(t) represents the horizontal distance traveled by the football and y(t) represents the height of the football above the ground at time t.

The initial velocity is split into its horizontal and vertical components using the trigonometric functions cosine and sine respectively. The horizontal component remains constant, while the vertical component is affected by gravity (the term -16t²) along with the initial vertical velocity.