7
QuizMultiple Choice

Graphing Parametric Equations

Question 7 • Precalculus

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?

Answer
A
x(t) = 59sin(45o)t and y(t) = –16t2 + 59cos(45o)t
B
x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t
C
x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t + 4
D
x(t) = 59sin(45o)t and y(t) = –16t2 + 59cos(45o)t + 4

Explanation

Resolve the initial velocity into horizontal and vertical components: the horizontal component is 59 cos(45°), and the vertical component is 59 sin(45°). Thus x(t) = 59 cos(45°)t, while vertical motion follows y(t) = −16t² + 59 sin(45°)t + 4, where −16t² accounts for gravity and 4 is the starting height. These equations match choice C.

AI-written and checked against the verified answer.

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