Suppose that a baseball is thrown at an angle of 30 ° with an initial speed of 88 ft/sec from an initial height of 3 ft . Choose a coordinate system with the origin at ground level directly under the point of release. a. Write parametric equations defining the path of the ball. b. When will the ball reach its highest point? c. Determine the coordinates of the ball at its highest point. Give the exact values and the coordinates rounded to the nearest tenth of a foot. d. If another player catches the ball at a height of 4 ft on the way down, how long was the ball in the air? Round to the nearest hundredth of a second. e. How far apart are the two players? Round to the nearest foot. f. Eliminate the parameter and write an equation in rectangular coordinates to represent the path of the ball.
Suppose that a baseball is thrown at an angle of 30 ° with an initial speed of 88 ft/sec from an initial height of 3 ft . Choose a coordinate system with the origin at ground level directly under the point of release. a. Write parametric equations defining the path of the ball. b. When will the ball reach its highest point? c. Determine the coordinates of the ball at its highest point. Give the exact values and the coordinates rounded to the nearest tenth of a foot. d. If another player catches the ball at a height of 4 ft on the way down, how long was the ball in the air? Round to the nearest hundredth of a second. e. How far apart are the two players? Round to the nearest foot. f. Eliminate the parameter and write an equation in rectangular coordinates to represent the path of the ball.
Solution Summary: The author calculates the parametric equation that represents the path of the ball if the baseball is thrown with an initial speed of 88ft/sec.
Suppose that a baseball is thrown at an angle of
30
°
with an initial speed of
88
ft/sec
from an initial height of
3
ft
. Choose a coordinate system with the origin at ground level directly under the point of release.
a. Write parametric equations defining the path of the ball.
b. When will the ball reach its highest point?
c. Determine the coordinates of the ball at its highest point. Give the exact values and the coordinates rounded to the nearest tenth of a foot.
d. If another player catches the ball at a height of
4
ft
on the way down, how long was the ball in the air? Round to the nearest hundredth of a second.
e. How far apart are the two players? Round to the nearest foot.
f. Eliminate the parameter and write an equation in rectangular coordinates to represent the path of the ball.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
=
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