HW 3 Phys 1403

A projectile is launched with an initial velocity of 80 m/s at 30° above the horizontal. Neglecting air resistance, what is horizontal component of the projectile's acceleration?

0 m/s2

A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s2?

0.160 s

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. How fast can she swim in still water?

0.50 m/s

A swimmer heading directly across a river that is 200 m wide reaches the opposite bank in 6 min 40 s. During this swim, she is swept downstream 480 m. What is the speed of the current?

1.2 m/s

A child is trying to throw a ball over a fence. She gives the ball an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground and the fence is 2.0 m high. The ball just clears the fence while still traveling upwards and experiences no significant air resistance. How far is the child from the fence?

1.6 m

You are traveling at 55 mi/h along the +x-axis relative to a straight, level road and pass a car that is traveling at 45 mi/h. The relative velocity of your car to the other car is

10 mi/h

The x component of vector A⃗ is 8.7 units, and its y component is -6.5 units. The magnitude of A⃗ is closest to

11 units

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 28.0 m/s horizontally in a city where the acceleration due to gravity is 9.81 m/s2. The puck experiences no significant air resistance as it falls. The height of the platform above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

12.6°

The components of vectors A⃗ and B⃗ are given as follows:Ax = 7.6 Bx = -5.1Ay = -9.2 By = -6.8What is the magnitude of the vector difference A⃗ −B⃗ ?

13

A ball thrown at an initial angle of 37.0∘ and initial velocity vi = 23.0 m/s reaches a maximum height h, as shown in (Figure 1). With what initial speed must a ball be thrown straight up to reach the same maximum height h?

13.8 m/s

A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is

157 m/s at an angle 7.31° south of east.

A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

18.1 m/s

Vector A⃗ has a magnitude of 7.0 m and points 30° east of north. Vector B⃗ has a magnitude of 5.0 m and points 30° west of south. The resultant vector A⃗ +B⃗ is given by

2.0 m at an angle 60° north of east.

Three vectors, S⃗ , T⃗ , and U⃗ have the components shown in the table. What is the magnitude of the resultant of these three vectors?

2.00 m

A hockey puck slides off the edge of a platform with an initial velocity of 20 m/s horizontally. The height of the platform above the ground is 2.0 m. What is the magnitude of the velocity of the puck just before it touches the ground? You can neglect air resistance.

21 m/s

A player throws a football 50.0 m at 61.0° north of west. What is the westward component of the displacement of the football?

24.2 m

A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector?

28 km

You throw a rock horizontally off a cliff with a speed of 20 m/s and no significant air resistance. After 2.0 s, the magnitude of the velocity of the rock is closest to

28 m/s

In a room where g = 9.81 m/s2, a hockey puck slides off the edge of a platform with an initial velocity of 28.0 m/s horizontally. The height of the platform above the ground is 2.00 m. What is the speed of the puck just before it hits the ground? The air resistance is negligibly small.

28.7 m/s

A football is kicked at an angle of 30 ∘ with a speed of 26 m/s . To the nearest second, how long will the ball stay in the air?

3 s

A car drives horizontally off a 71-m-high cliff at a speed of 37 m/s . Ignore air resistance. How long will it take the car to hit the ground? How far from the base of the cliff will the car hit?

3.8 s, 140 m

A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what angle was the projectile fired above the horizontal?

30°

The x component of vector A⃗ is 5.3 units, and its y component is -2.3 units. The angle that vector A⃗ makes with the +x-axis is closest to

340∘

An athlete participates in an interplanetary discus throw competition during an Olympiad that takes place on a planet where the acceleration due to gravity is 9.7 m/s2. He throws the discus with an initial velocity of 20 m/s at an angle of 60° from the vertical. Neglecting air resistance and the height of the discus at the point of release, what is the range of the discus?

36 m

A displacement vector is 34.0 m in length and is directed 60.0° east of north. Selecting from the choices in the table below, what are the components of this vector? 1 29.4 m 17.0 m 2 18.2 m 28.1 m 3 22.4 m 11.5 m 4 17.0 m 29.4 m 5 25.2 m 18.2 m

4

Four vectors, A⃗ , B⃗ , C⃗ , and D⃗ , are shown in the figure. The sum of these four vectors is a vector having magnitude and direction

4.0 cm, along -y-axis.

When Jeff ran up a hill at 7.0 m/s, the horizontal component of his velocity vector was 5.1 m/s. What was the vertical component of Jeff's velocity?

4.8 m/s

A football is kicked at an angle of 25 ∘ with a speed of 23 m/s . How far will the ball travel?

41 m

A boy throws a ball with an initial velocity of 25 m/s at an angle of 30° above the horizontal. If air resistance is negligible, how high above the projection point is the ball after 2.0 s?

5.4 m

A plane flies directly from city A to city B, which are separated by 2300 mi. From A to B, the plane flies into a 65 mi/h headwind. On the return trip from B to A, the wind velocity is unchanged. The trip from B to A takes 65 min less than the trip from A to B. What is the airspeed (assumed constant) of the plane relative to the air (that is, the airspeed)?

530 mi/h

Formula One race cars are capable of remarkable accelerations when speeding up, slowing down, and turning corners. At one track, cars round a corner that is a segment of a circle of radius 95 m at a speed of 68 m/s. What is the approximate magnitude of the centripetal acceleration, in units of g?

5g

The acceleration due to gravity on the Moon is only one-sixth of that on Earth, and the Moon has no atmosphere. If you hit a baseball on the Moon with the same effort (and therefore at the speed and angle) as on Earth, how far would the ball would travel on the Moon compared to on Earth? Neglect air resistance on Earth.

6 times as far as on Earth

An object moves with a constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object?

6.0 m/s2

Three vectors, S⃗ , T⃗ , and U⃗ , have the components shown in the table. What angle does the resultant of these three vectors make with the +x-axis?

66∘ below the +x-axis

Vector A⃗ has magnitude 2 units and is directed to the north. Vector B⃗ has magnitude 5 units and is directed to the south. Calculate the magnitude and direction of A⃗ −B⃗ .

7 units, north

Vector A⃗ has a magnitude of 6.0 m and points 30° south of east. Vector B⃗ has a magnitude of 4.0 m and points 30° west of south. The resultant vector A⃗ +B⃗ is given by

7.2 m at an angle of 64° south of east.

An airplane undergoes the following displacements, all at the same altitude: First, it flies 59.0 km in a direction 30.0° east of north. Next, it flies 58.0 km due south. Finally, it flies 100 km 30.0° north of west. Use components to determine how far the airplane ends up from its starting point.

71.5 km

On a calm day with no wind, you can run a 1500-m race at a velocity of 4.0 m/s. If you run the same race on a day when you have a constant headwind that slows your speed by 2.0 m/s, how much time would it take you to finish the race?

750 s

A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of the circular section of a dive. What is the radius of curvature of this section of the dive?

9.2 km

Vector A⃗ has a magnitude of 6.0 m and points 30° north of east. Vector B⃗ has a magnitude of 4.0 1901259 and points 30∘ east of north. The resultant vector A⃗ +B⃗ is given by

9.7 m at an angle of 42∘ north of east

A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stopwatch measures the stone's trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff if air resistance is negligibly small?

91 m

The magnitude of A⃗ is 5.5 m, and this vector lies in the second quadrant and makes an angle of 34∘ with the +y-axis. The components of A⃗ are closest to: Ax = 4.6 m, Ay = -3.1 m . Ax = -4.6 m, Ay = 3.1 m . Ax = 3.1 m, Ay = -4.6 m . Ax = -3.1 m, Ay = 4.6 m . Ax = -4.6 m, Ay = -3.1 m . Previous Answers Correct Provide Feedback

Ax = -3.1 m, Ay = 4.6 m.

Which vector best represents the car's velocity at position 1? Which vector best represents the car's acceleration at point 1? Which vector best represents the car's velocity at position 2? Which vector best represents the car's acceleration at point 2? Which vector best represents the car's velocity at position 3? Which vector best represents the car's acceleration at point 3?

B, E, C, D, B, A

Which combination of the vectors shown in (Figure 1) has the largest magnitude?

B⃗ +A⃗ −C⃗

Which vector best represents the ball's velocity at position 2? Which vector best represents the ball's acceleration at position 2? Which vector best represents the ball's velocity at position 3? Which vector best represents the ball's acceleration at position 3?

D, A, C, A

Which combination points directly upward?

P⃗ +Q⃗

A car goes around a corner in a circular arc at constant speed. Select a motion diagram including positions, velocity vectors, and acceleration vectors.

a points inward v is in direction of movement