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.
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY