How many rows of seats are needed to seat 673 people at a concert when the rows seat 37 people each?
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An object that is in motion as a projectile follows a path or trajectory of a parabola
The function and values are;
- a) The equation of the quadratic function is;
- b) The maximum height of the ball is approximately <u>7.334 m</u>
- c) Horizontal distance at maximum height <u>18.8 meters</u>
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Reason:
a) Known parameters are;
Let f(x) = a·x² + b·x + c represent the equation of the parabola modelling the path of the ball, we have;
Points on the path of the parabola = (0, 0), (35, 1.5), 37, 0)
Plugging the values gives;
0 = a·0² + b·0 + c
Therefore, c = 0
1.5 = 35²·a + 35·b
0 = 37²·a + 37·b
Solving gives;
a = -3/140, b = 111/140
The equation of the quadratic function is therefore;
b) The maximum height is given by the vertex of the parabola
The x-coordinate at the vertex is the point
Which gives;
The maximum height is therefore;
The maximum height of the ball is approximately 7.334 m
c) The distance the ball has travelled to horizontally is given by half of the range, <em>R</em> as follows;
The range of the motion, R = 37 meters
Therefore;
The distance the ball has travelled horizontally to reach the maximum height horizontally <u>18.5 meters</u>
Learn more about the trajectory of a projectile here: