A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25 ° . The height of the ball can be modeled by h t = − 16 t 2 + 30.4 t + 5 , where h t is the height (in ft) and t is the time in seconds after release. a. Determine the time at which the ball will be at its maximum height. b. Determine the maximum height of the ball. c. Determine the amount of time required for the bail to reach the receiver's hands if the receiver catches the ball at a point 3 ft off the ground.
A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of 25 ° . The height of the ball can be modeled by h t = − 16 t 2 + 30.4 t + 5 , where h t is the height (in ft) and t is the time in seconds after release. a. Determine the time at which the ball will be at its maximum height. b. Determine the maximum height of the ball. c. Determine the amount of time required for the bail to reach the receiver's hands if the receiver catches the ball at a point 3 ft off the ground.
Solution Summary: The author explains how the arc of the parabolic curve of a quadratic function, h(t), will open downwards and the vertex coordinates will provide the maximum values
A quarterback throws a football with an initial velocity of 72 ft/sec at an angle of
25
°
.
The height of the ball can be modeled by
h
t
=
−
16
t
2
+
30.4
t
+
5
, where
h
t
is the height (in ft) and
t
is the time in seconds after release.
a. Determine the time at which the ball will be at its maximum height.
b. Determine the maximum height of the ball.
c. Determine the amount of time required for the bail to reach the receiver's hands if the receiver catches the ball at a point 3 ft off the ground.
4
In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and
evaluate the integral. Hint: Find the limits on r and s by sketching the area of integration in the (x, y) plane along
with the r and s axes, and then show that the same area can be covered by s from 0 to r and r from 0 to 1.
7. What are all values of 0, for 0≤0<2л, where 2 sin² 0=-sin?
-
5π
6
π
(A) 0, л,
and
6
7π
(B) 0,л,
11π
, and
6
6
π 3π π
(C)
5π
2 2 3
, and
π 3π 2π
(D)
2' 2'3
, and
3
4元
3
1
די
}
I
-2m
3
1
-3
บ
1
#
1
I
3#
3m
8. The graph of g is shown above. Which of the following is an expression for g(x)?
(A) 1+ tan(x)
(B) 1-tan (x)
(C) 1-tan (2x)
(D) 1-tan
+
X
-
9. The function j is given by j(x)=2(sin x)(cos x)-cos x. Solve j(x) = 0 for values of x in the interval
Quiz A: Topic 3.10
Trigonometric Equations and Inequalities
Created by Bryan Passwater
can you solve this question using the right triangle method and explain the steps used along the way
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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