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A soccer ball on the ground is kicked with an initial velocity of 37 feet per second at an elevation angle of 70°. Which parametric equations represent the path of the soccer ball?

A: x(t) = 37cos(70o)t and y(t) = –16t2 + 37sin(70o)t
B: x(t) = 37sin(70o)t and y(t) = –16t2 + 37cos(70o)t
C: x(t) = 37cos(70o)t and y(t) = –16t2 + sin(70o)t + 37
D: x(t) = 37sin(70o)t and y(t) = –16t2 + cos(70o)t + 37

Sagot :

whitvicc

Answer: It’s A

Step-by-step explanation: Got it right on the quiz edg2021

The parametric equations represent the path of the soccer ball is

[tex]x = 37cos(70)t[/tex]  and [tex]y = 37sin(70)t - 16t^{2}[/tex]

What is projectile motion?

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory.

projection motion formula :

Position at time t

x = ([tex]v_{0}[/tex] cosθ)t  

y = ([tex]v_{0}[/tex] sinθ)t – 1/2 g[tex]t^{2}[/tex]  

According to the question

A soccer ball on the ground is kicked

initial velocity ([tex]v_{0}[/tex])= 37 feet per second

elevation angle = 70°

using projection motion formula :

Position at time t

g = 9.8 m/[tex]sec^{2}[/tex] = 32 ft/[tex]sec^{2}[/tex]

x = ([tex]v_{0}[/tex] cosθ)t  

[tex]y = v_{0} sin[/tex]θ[tex]t[/tex][tex]-\frac{1}{2} gt^{2}[/tex]

substituting the value [tex]v_{0}= 37[/tex] and θ = 70 degrees in the above formula

[tex]x = 37cos(70)t[/tex] 

[tex]y= 37sin(70)t -\frac{1}{2} ( 32)t^{2}[/tex]

[tex]y = 37sin(70)t - 16t^{2}[/tex]

Hence,  the parametric equations represent the path of the soccer ball is

[tex]x = 37cos(70)t[/tex]  and

[tex]y = 37sin(70)t - 16t^{2}[/tex]

To know more about projectile motion here:

https://brainly.com/question/11049671

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