6. A picture 40 cm high is placed on a wall with its based 30 cm above the level of the eye of an observer. If the observer is approaching the wall at the rate of 40 cm/s, how fast is the measure of the angle subtended at the

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Ans. -9.17lb/ft per second
6. A picture 40 cm high is placed on a wall with its based 30 cm above the
level of the eye of an observer. If the observer is approaching the wall at
the rate of 40 cm/s, how fast is the measure of the angle subtended at the
217
MATH 401 - DIFFERENTIAL CALCULUS
observer's eye by the picture changing when the observer is 1 m from the
wall?
Ans. 0.08 rad/s
7. Suppose we have two resistors with resistances R1 and R2 measured in
ohms(0) connected in parallel. The equivalent resistance, R, iis then given
by
1
1
RR,"R,
Supposed R, is increasing at a rate of 0.4N/min and R, is decreasing at a
rate of 0.70/min . At what rate is R changing when R, = 800 and
R2 = 1050?
Ans. -0.002 1/min
8. A man 6 feet tall walks at a rate of 5 feet per second away from the light
that is 15 feet above the ground. When he is 10 feet from the base of the
light,
Ans플/t/s
(b)At what rate is the length of his shadow moving? Ans." ft/s
(a) At what rate is the tip of his shadow moving?
10
9. A particle is moving along a line according to the equation of motion
4t
*i+1
Where s meters is the directed distance of the particle from the origin at t
seconds. Find the t, s, and velocity v when the acceleration a = 0.
Ans. t = 1s s= 2.5 m v = 2 m/s
10. A stone is dropped from a building 256 ft high. How long it takes the stone
to reach the ground? What is the velocity of the stone when it reaches the
ground?
Ans. t = 4s
v = -128 ft/s
Transcribed Image Text:Ans. -9.17lb/ft per second 6. A picture 40 cm high is placed on a wall with its based 30 cm above the level of the eye of an observer. If the observer is approaching the wall at the rate of 40 cm/s, how fast is the measure of the angle subtended at the 217 MATH 401 - DIFFERENTIAL CALCULUS observer's eye by the picture changing when the observer is 1 m from the wall? Ans. 0.08 rad/s 7. Suppose we have two resistors with resistances R1 and R2 measured in ohms(0) connected in parallel. The equivalent resistance, R, iis then given by 1 1 RR,"R, Supposed R, is increasing at a rate of 0.4N/min and R, is decreasing at a rate of 0.70/min . At what rate is R changing when R, = 800 and R2 = 1050? Ans. -0.002 1/min 8. A man 6 feet tall walks at a rate of 5 feet per second away from the light that is 15 feet above the ground. When he is 10 feet from the base of the light, Ans플/t/s (b)At what rate is the length of his shadow moving? Ans." ft/s (a) At what rate is the tip of his shadow moving? 10 9. A particle is moving along a line according to the equation of motion 4t *i+1 Where s meters is the directed distance of the particle from the origin at t seconds. Find the t, s, and velocity v when the acceleration a = 0. Ans. t = 1s s= 2.5 m v = 2 m/s 10. A stone is dropped from a building 256 ft high. How long it takes the stone to reach the ground? What is the velocity of the stone when it reaches the ground? Ans. t = 4s v = -128 ft/s
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