math
NAME: __________________________________________________________________________
1.
Find the equation of a tangent line that is tangent to the function
2.
Find the equation of a line that is perpendicular to the tangent line of a function and it also passes through the same tangent point
(Hint: the slopes of 2 perpendicular lines are opposite and reciprocal to each other)
3.
Find the equation of a tangent line that is tangent to the curve .
4.
A ball is tossed vertically up in the air from a roof of a building 240 foot tall with the initial velocity of 64 feet per second. The position of the ball in the air after t seconds is represented by the function where h : height of the ball in the air after t seconds. Where t : time and, initial velocity and initial height respectively.
a. What is the velocity and acceleration of the ball in the air after 5 seconds?
(the acceleration measures the rate change of the velocity ) Ans: -96 ft/sec and -32 ft/
b.
When does the ball hit the ground and what is the velocity of the moment of impact? Ans: After seconds and the velocity of impact is -139.52ft per second.
33
(,)
pp
-
2
3
(:)
ansyx
p
=+
23
40,(2,1)
xyat
-=
1
3
(:(1))
ansyx
=+
2
00
()16
httvth
=-++
00
&:
vh
()
at
()
vt
2
sec
476
2
6.36
+
»
(
)
2
62,1
xxyat
+=
5
2
(:6)
ansyx
=-+
cos(3)
yxy
=