Chapter 10 Practice Test

Question 1

You are throwing paper airplanes in class, and you throw them hard enough they start out at a horizontal speed of 10 ft / s. However, they have a horizontal deceleration of 4 ft / s. What is the greatest distance away from the intial position that an object can be if it can be struck by the airplane?

Answer 1

12 1/2ft

Question 2

A penny is thrown down with a velocity of 3/2 ft/s off the top of the Spears Tower, which is 1500 feet tall. The penny accelerates at 3e 2t ft/s2 as it falls. What is its velocity when it hits the ground?

Answer 2

−3001 1/2 ft/s

Question 3

I am stuck in Austin with a flat tire, and I need to get to my class in Houston within 2 hours. The drive is 180 miles long, but I want to be careful of the Austin cops. I do not usually get caught speeding unless I am seen accelerating too fast, so I do not want to accelerate at a rate of more than 120 mi / h2. Just to be careful, I′m going to take exactly 2 hours to make the trip. Assuming I accelerate at 120 mi / h2 for a while, and travel at a constant speed afterwards, what’s the fastest speed I′ll be going during my trip?

Answer 3

120 mi / h

Question 4

A skydiver jumps out of a plane 7400 feet above the earth’s surface, so that she is not moving up or down as she leaves the plane. She has to open her parachute before she is 1000 feet above the surface to make a safe landing. How long can she wait to open her parachute?

Answer 4

20 s

Question 5

What is the area of the region bounded by the curves y = x^ 3 − x and y = 7x − x ^3?

Answer 5

16

Question 6

Evaluate ∫∞−∞2x(1+x2)2dx

Answer 6

0

Question 7

What is the area between y=√x+2 and y=−3x+6 from x=0 to x=1 ?

Answer 7

11/6

Question 8

What is the area between the curves y=cosx+3 and y=sinx−1 from x=−π to x=3π ?

Answer 8

16π

Question 9

What is the area between the curves x=y and y=x3 from y=−1 to y=1 ?

Answer 9

1/2

Question 10

What is the area between the curve x=√16−y^2 and the y-axis ?

Answer 10

8π

Question 11

What is the average value of 1/x on [1, 5]?

Answer 11

ln(5)/4

Question 12

What is the average value of 2−x−x^2 on [0, 2]?

Answer 12

-1/3

Question 13

What is the volume of the solid whose cross-sections are squares perpendicular to the x-axis and with one side of the region bounded by curves y=x and y=√x ?

Answer 13

1/30

Question 14

What is the volume of the solid whose cross-sections are equilateral triangles perpendicular to the x-axis and with bases on the region bounded by curves y=x2+1, x=1, and x-axis and the y-axis.

Answer 14

7√3/15

Question 15

What is the volume of the solid of revolution obtained by rotating the region bounded by x = 1, x = 2, y = 0, and y = x 2 around the x-axis?

Answer 15

31π/5

Question 16

Find the volume of the solid of revolution obtained by rotating the region bounded by
y=√x and y=x2 about the y-axis.

Answer 16

3π/10

Question 17

Find the volume of the solid of revolution obtained by rotating the region bounded by
x = 1, x = 2, y = x 3, and y = 5x + 2
about the y-axis.

Answer 17

254π/15

Question 18

A tank shown is full of liquid with density 1 lb/m3. What is the work done in pumping the liquid out of the tank from the top outlet? (Use the formula F = ma (force equals mass times acceleration) and the acceleration of gravity g = 9.8 m/s2 to solve this problem.)

Answer 18

2450 m-lb

Question 19

Suppose 4 m-lb of work are needed to stretch a spring 14 cm from its natural position. How much work is needed to stretch it 20 cm from its natural position?

Answer 19

8.16 m-lb

Question 20

Find the center of the triangular lamina defined by the following region: x = 0, y = 0, x + y = 1.

Answer 20

(1/3, 1/3)

Question 21

Find the center of mass of the lamina bounded by f (x) = x 2 + 1 over [−1, 1).

Answer 21

(0, 7/10)

Question 22

Find the center of mass of the lamina of triangular shape with boundaries given by
y = 1 − x, y = 1 + x and the x-axis.

Answer 22

(0, 1/3)

Question 23

Compute the length of the arc

f(x)=x33+14x,x∈[1,2].

Answer 23

59/24

Question 24

Compute the length of the arc

f(x)=−cosx+14ln|cotx+cscx|,x∈[π6,π2].

Answer 24

√3/2−1/4ln(2−√3)

Question 25

What is the area of the region bounded by the curves y = x 4 + x 3 − 2x + 3 and y = x 3 + 4x 2 − 2x + 3?

Answer 25

128/15