Question 1

A car rounds a 20-m radius curve at a speed of 10 m/s.The magnitude of its acceleration is: A)0 m/s² B)0.20 m/s² C)5.0 m/s² D)40 m/s² E)400 m/s²

Accepted Answer

We can use the formula a = v^2/r, where a is the magnitude of acceleration, v is the speed, and r is the radius of the curve. Plugging in the given values, we get a = (10 m/s)^2 / 20 m = 5 m/s^2. Therefore, the correct answer is (C) 5.0 m/s^2.

Question 2

A ferry boat is sailing at 12 km/h 30$\degree$ W of N with respect to a river that is flowing at 6.0 km/h E.As observed from the shore, the ferry boat is sailing:
A)30$\degree$ E of N
B)due N
C)30$\degree$ W of N
D)45$\degree$ E of N
E)none of these

Accepted Answer

The answer of A ferry boat is sailing at 12...

Question 3

A girl wishes to swim across a river to a point directly opposite as shown.She can swim at 2 m/s in still water and the river is flowing at 1 m/s.At what angle $\theta$ with respect to the line joining the starting and finishing points should she swim? 
A)30 $\degree$
B)45 $\degree$
C)60 $\degree$
D)63 $\degree$
E)90 $\degree$

Accepted Answer

The answer of A girl wishes to swim across a...

Question 4

For a biological sample in a 1.0-m radius centrifuge to have a centripetal acceleration of 25g its speed must be:
A)11 m/s
B)16 m/s
C)50 m/s
D)122 m/s
E)245 m/s

Accepted Answer

The answer of For a biological sample in a 1.0-m...

Question 5

A stone is tied to the end of a string and is swung with constant speed around a horizontal circle with a radius of 1.5 m.If it makes two complete revolutions each second, its acceleration is: A)0.24 m/s² B)2.4 m/s² C)24 m/s² D)240 m/s² E)2400 m/s²

Accepted Answer

The answer of A stone is tied to the end...

Question 6

A boat is traveling upstream at 14 mph with respect to a river that is flowing at 6 mph (with respect to the ground).A man runs directly across the boat, from one side to the other, at 6 mph (with respect to the boat).The speed of the man with respect to the ground is:
A)10 mph
B)14 mph
C)18.5 mph
D)21 mph
E)26 mph

Accepted Answer

The answer of A boat is traveling upstream at 14...

Question 7

A boy wishes to cross a river in the shortest possible time, without necessarily landing directly across from his starting point.He can row at 2 m/s in still water and the river is flowing at 1 m/s.At what angle $\theta$ should he point the bow (front)of his boat? 
A)30 $\degree$
B)45 $\degree$
C)60 $\degree$
D)63 $\degree$
E)90 $\degree$

Accepted Answer

The answer of A boy wishes to cross a river...

Question 8

A boat is able to move through still water at 20 m/s.It makes a round trip to a town 3.0 km upstream.If the river flows at 5 m/s, the time required for this round trip is:
A)120 s
B)150 s
C)200 s
D)300 s
E)320 s

Accepted Answer

The speed of the boat in still water is 20 m/s, and the speed of the river is 5 m/s. When going upstream, the effective speed of the boat is $20 - 5 = 15$ m/s, and when going downstream, it is $20 + 5 = 25$ m/s. The distance to the town is 3.0 km, which is 3000 m. The time to go upstream is $3000 m / 15 m/s = 200$ s, and the time to go downstream is $3000 m / 25 m/s = 120$ s. The total time for the round trip is $200 s + 120 s = 320$ s.

Question 9

A Ferris wheel with a radius of 8.0m makes 1 revolution every 10 s.When he is at the top, essentially a diameter above the ground, he releases a ball.How far from the point on the ground directly under the release point does the ball land?
A)0 m
B)1.0 m
C)8.0 m
D)9.1 m
E)16 m

Accepted Answer

Since the Ferris wheel makes 1 revolution in 10 seconds, its angular velocity is 2π/10 = π/5 radians/s. 
When the ball is released at the top, it will have the same horizontal velocity as the Ferris wheel, which is v = rω = 8π/5 m/s. 
The time of flight, T, can be found using the equation y = vyt + 1/2gt^2, where y is the initial vertical displacement (8m) and vy is the initial vertical velocity (0). 
Solving for T gives T = sqrt(16/5) s. 
The horizontal distance traveled by the ball, x, is given by x = vt = (8π/5)(sqrt(16/5)) = 9.1m (rounded to one decimal place). 
Therefore, the ball lands 9.1m from the point on the ground directly under the release point. The answer is (D) 9.1m.

Question 10

A girl jogs around a horizontal circle with a constant speed.She travels one fourth of a revolution, a distance of 25 m along the circumference of the circle, in 5.0 s.The magnitude of her acceleration is: A)0.31 m/s² B)1.3 m/s² C)1.6 m/s² D)3.9 m/s² E)6.3 m/s²

Accepted Answer

The distance traveled by the girl in one fourth of revolution is 25 m. Therefore, the total circumference of the circle is:

C = 25m / (1/4) = 100m

The time taken to travel this distance is 5.0 s. Therefore, the speed of the girl is:

v = d/t = 25m / 5.0s = 5 m/s

The acceleration of the girl is given by:

a = v^2/r

where r is the radius of the circle.

The radius of the circle can be calculated as:

r = C/2π = 100m / (2π) = 15.92m

Substituting the values of v and r, we get:

a = v^2/r = (5 m/s)^2 / 15.92m = 1.57 m/s^2 ≈ 1.6 m/s^2

Therefore, the magnitude of her acceleration is 1.6 m/s^2, which is closest to option C.

Question 11

A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle.The acceleration at the bottom of the circle is: A)9.8 m/s², up B)9.8 m/s², down C)8.0 m/s², up D)32 m/s², up E)32 m/s², down

Accepted Answer

The answer of A stone is tied to a 0.50-m...

Question 12

A motor boat can travel at 10 km/h in still water.A river flows at 5 km/h west.A boater wishes to cross from the south bank to a point directly opposite on the north bank.At what angle must the boat be headed?
A)27$\degree$ E of N
B)30$\degree$ E of N
C)45$\degree$E of N
D)60$\degree$ E of N
E)depends on the width of the river

Accepted Answer

The answer of A motor boat can travel at 10...

Question 13

A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle.Its acceleration at the top of the circle is: A)9.8 m/s², up B)9.8 m/s², down C)8.0 m/s², down D)32 m/s², up E)32 m/s², down

Accepted Answer

The answer of A stone is tied to a 0.50-m...

Quiz 4: Motion in Two and Three Dimensions

A car rounds a 20-m radius curve at a speed of 10 m/s.The magnitude of its acceleration is:

A ferry boat is sailing at 12 km/h 30 $\degree$ W of N with respect to a river that is flowing at 6.0 km/h E.As observed from the shore, the ferry boat is sailing:

For a biological sample in a 1.0-m radius centrifuge to have a centripetal acceleration of 25g its speed must be:

A stone is tied to the end of a string and is swung with constant speed around a horizontal circle with a radius of 1.5 m.If it makes two complete revolutions each second, its acceleration is:

A boat is traveling upstream at 14 mph with respect to a river that is flowing at 6 mph (with respect to the ground) .A man runs directly across the boat, from one side to the other, at 6 mph (with respect to the boat) .The speed of the man with respect to the ground is:

A boat is able to move through still water at 20 m/s.It makes a round trip to a town 3.0 km upstream.If the river flows at 5 m/s, the time required for this round trip is:

A Ferris wheel with a radius of 8.0m makes 1 revolution every 10 s.When he is at the top, essentially a diameter above the ground, he releases a ball.How far from the point on the ground directly under the release point does the ball land?

A girl jogs around a horizontal circle with a constant speed.She travels one fourth of a revolution, a distance of 25 m along the circumference of the circle, in 5.0 s.The magnitude of her acceleration is:

A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle.The acceleration at the bottom of the circle is:

A motor boat can travel at 10 km/h in still water.A river flows at 5 km/h west.A boater wishes to cross from the south bank to a point directly opposite on the north bank.At what angle must the boat be headed?

A stone is tied to a 0.50-m string and whirled at a constant speed of 4.0 m/s in a vertical circle.Its acceleration at the top of the circle is: