a. i. The parametric equation for the horizontal movement is x = 43.84t
ii. The parametric equation for the vertical movement is y = 50 + 43.84t
b. the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)
<h2>a. Parametric equations</h2>
A parametric equation is an equation that defines a set of quantities a functions of one or more independent variables called parameters.
<h3>i. Parametric equation for the horizontal movement</h3>
The parametric equation for the horizontal movement is x = 43.84t
Since
- the angle of elevation is Ф = 45° and
- the initial velocity, v = 62 ft/s,
the horizontal component of the velocity is v' = vcosФ.
So, the horizontal distance the football moves in time, t is x = vcosФt
= vtcosФ
= 62tcos45°
= 62t × 0.7071
= 43.84t
So, the parametric equation for the horizontal movement is x = 43.84t
<h3>ii Parametric equation for the vertical movement</h3>
The parametric equation for the vertical movement is y = 50 + 43.84t
Also, since
- the angle of elevation is Ф = 45° and
- the initial velocity, v = 62 ft/s,
the vertical component of the velocity is v" = vsinФ.
Since the football is initially at a height of h = 50 feet, the vertical distance the football moves in time, t relative to the ground is y = 50 + vsinФt
= 50 + vtcosФ
= 50 + 62tsin45°
= 50 + 62t × 0.7071
= 50 + 43.84t
<h3>b. Location of football at maximum height relative to starting point</h3>
The location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)
Since the football reaches maximum height at t = 1.37 s
The x coordinate of its location at maximum height is gotten by substituting t = 1.37 into x = 48.84t
So, x = 43.84t
x = 43.84 × 1.37
x = 60.0608
x ≅ 60.1 ft
The y coordinate of the football's location at maximum height relative to the ground is y = 50 + 48.84t
The y coordinate of the football's location at maximum height relative to the starting point is y - 50 = 48.84t
So, y - 50 = 48.84t
y - 50 = 43.84 × 1.37
y - 50 = 60.0608
y - 50 ≅ 60.1 ft
So, the location of the football at its maximum height relative to the starting point is (60.1 ft, 60.1 ft)
Learn ore about parametric equations here:
brainly.com/question/8674159
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