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An airplane is traveling \( 900. \) \( \text{km/h} \) in a direction \( 38.5^{\circ} \) west of north.

Vector \( A \) is \( 44.0 \) units and \( 28.0^{\circ} \) above the \( +x \) axis, vector \( B \) is \( 26.5 \) units and \( 56.0^{\circ} \) above the \( -x \) axis, and vector \( C \) is \( 31.0 \) units along the \( -y \) axis. Determine the resultant (sum) of the three vectors.

A skier is accelerating down a \( 30.0^{\circ} \) hill at \( 3.80 \) \( \text{m/s}^2 \).

Vector \( V_1 \) is \( 6.0 \) units long and points along the negative \( y \) axis. Vector \( V_2 \) is \( 4.5 \) units long and points at \( +45^{\circ} \) to the positive \( x \) axis.

An object is moving to the west at a constant speed. Three forces are exerted on the object. One force is \( 10 \) \( \text{N} \) directed due north, and another is \( 10 \) \( \text{N} \) directed due west. What is the magnitude and direction of the third force if the object is to continue moving to the west at a constant speed?

Does the odometer of a car measure a scalar or a vector quantity? What about the speedometer?

Two cannonballs, A and B, are fired from the ground with identical initial speeds, but with \( \theta_A \) larger than \( \theta_B \).

The magnitude of a component of a vector must be

You are adding vectors of length \( 20 \) and \( 40 \) units. Which of the following choices is a possible resultant magnitude?

Which statements are not valid for a projectile? Take up as positive.

Seo-Jun throws a ball to her friend Zuri. The ball leaves Seo-Jun’s hand from a height \( h = 1.5 \) \( \text{m} \) above the ground with an initial speed \( \vec{v}_{s,0} = 12 \) \( \text{m/s} \) at an angle of \( \theta = 25^\circ \) with respect to the horizontal. Zuri catches the ball at a height of \( h = 1.5 \) \( \text{m} \) above the ground, as shown in the figure.After catching the ball, Zuri throws it back to Seo-Jun. The ball leaves Zuri’s hand from a height \( h = 1.5 \) \( \text{m} \) above the ground. The ball is moving with a speed of \( 15 \) \( \text{m/s} \) when it reaches a maximum height of \( 5.8 \) \( \text{m} \) above the ground.At what height \( h’ \) above the ground will the ball be when the return throw reaches Seo-Jun?

A boat can row across a still \( 1 \, \text{km} \) wide river at a maximum speed of \( 5 \, \text{km/hr} \). If a current of \( 4 \, \text{km/hr} \) flows east as you try to directly cross the river, how long would it take?

You are piloting a small plane, and you want to reach an airport \(450 \, \text{km}\) due south in \(3.0 \,\text{hours}\). A wind is blowing from the west at \(50.0 \,\text{km/h}\). What heading and airspeed should you choose to reach your destination in time?

While Santa was delivering presents to the children of Nashville, Tennessee he experienced a strong wind perpendicular to his motion.

Gregory was walking through the halls of the school when he realized that he was walking in perpendicular directions and he could easily calculate his displacement using the incredibly useful techniques he learned in physics. He recognized that he walked 12.5 meters left and then 18.9 meters down. How far must he walk to the right so that his resultant displacement is 20.1 m?

A boat is rowed directly upriver at a speed of 2.5 m/s relative to the water. Viewers on the shore find that it is moving at only 0.5 m/s relative to the shore. What is the speed of the river? Is it moving with or against the boat?

A person is standing at the edge of the water and looking out at the ocean. The height of the person’s eyes above the water is \( h = 1.8 \, \text{m} \), and the radius of the Earth is \( R = 6.38 \times 10^6 \, \text{m} \). How far is it to the horizon (in meters)? In other words, find the distance \( d \) from the person’s eyes to the horizon. (Note: At the horizon, the angle between the line of sight and the radius of the Earth is \( 90^\circ \).)

Two racing boats set out from the same dock and speed away at the same constant speed of 101 km/h for half an hour (0.500 hr). Boat 1 is headed 27.6° south of west, and Boat 2 is headed 35.3° south of west. During this half-hour calculate…

A seagull first flies \( 160 \, \text{m} \) North, then heads \( 120.65 \, \text{m} \) at \( 18.43^\circ \) North of West. After you land:

Determine the sum of the three vectors given below. Give the resultant \( \vec{R} \) in terms of: (a) Vector components (b) Resultant vector Vectors: \( \vec{A} = 26.5 \, \text{m} \) @ \( 56^\circ \) NW \( \vec{B} = 44 \, \text{m} \) @ \( 28^\circ \) NE \( \vec{C} = 31 \, \text{m} \) South

All Resources

Everything you need to master Physics — for free.

AI Problem Solver

Meet Phy. The world's most advanced AI helper.

UBQ

1000+ Physics problems + AI help to supercharge learning.

Speed Reviews

8 AP Physics units condensed into 8 short review guides.

AP Phys. Exam Prep

Proven tips, tricks, and hacks to help you score that coveted 5.

Learn from Scratch

Learn Physics, from scratch, at your own pace.

Elite 1-to-1 Coaching

Guaranteed performance boost in scores and understanding.

AP Exam Prep

5 weeks for a 5. Expedited progress. Stellar Results.

Learn AP Physics

1-to-1 lessons covering AP Physics from start to end.

All Other Programs

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What we found:

An airplane is traveling \( 900. \) \( \text{km/h} \) in a direction \( 38.5^{\circ} \) west of north.

Vector \( A \) is \( 44.0 \) units and \( 28.0^{\circ} \) above the \( +x \) axis, vector \( B \) is \( 26.5 \) units and \( 56.0^{\circ} \) above the \( -x \) axis, and vector \( C \) is \( 31.0 \) units along the \( -y \) axis. Determine the resultant (sum) of the three vectors.

A skier is accelerating down a \( 30.0^{\circ} \) hill at \( 3.80 \) \( \text{m/s}^2 \).

Vector \( V_1 \) is \( 6.0 \) units long and points along the negative \( y \) axis. Vector \( V_2 \) is \( 4.5 \) units long and points at \( +45^{\circ} \) to the positive \( x \) axis.

Does the odometer of a car measure a scalar or a vector quantity? What about the speedometer?

Two cannonballs, A and B, are fired from the ground with identical initial speeds, but with \( \theta_A \) larger than \( \theta_B \).

The magnitude of a component of a vector must be

You are adding vectors of length \( 20 \) and \( 40 \) units. Which of the following choices is a possible resultant magnitude?

Which statements are not valid for a projectile? Take up as positive.

A boat can row across a still \( 1 \, \text{km} \) wide river at a maximum speed of \( 5 \, \text{km/hr} \). If a current of \( 4 \, \text{km/hr} \) flows east as you try to directly cross the river, how long would it take?

You are piloting a small plane, and you want to reach an airport \(450 \, \text{km}\) due south in \(3.0 \,\text{hours}\). A wind is blowing from the west at \(50.0 \,\text{km/h}\). What heading and airspeed should you choose to reach your destination in time?

While Santa was delivering presents to the children of Nashville, Tennessee he experienced a strong wind perpendicular to his motion.

A boat is rowed directly upriver at a speed of 2.5 m/s relative to the water. Viewers on the shore find that it is moving at only 0.5 m/s relative to the shore. What is the speed of the river? Is it moving with or against the boat?

Two racing boats set out from the same dock and speed away at the same constant speed of 101 km/h for half an hour (0.500 hr). Boat 1 is headed 27.6° south of west, and Boat 2 is headed 35.3° south of west. During this half-hour calculate…

A seagull first flies \( 160 \, \text{m} \) North, then heads \( 120.65 \, \text{m} \) at \( 18.43^\circ \) North of West. After you land:

Determine the sum of the three vectors given below. Give the resultant \( \vec{R} \) in terms of: (a) Vector components (b) Resultant vector Vectors: \( \vec{A} = 26.5 \, \text{m} \) @ \( 56^\circ \) NW \( \vec{B} = 44 \, \text{m} \) @ \( 28^\circ \) NE \( \vec{C} = 31 \, \text{m} \) South

Nerd Notes

Discover the world's best Physics resources

Everything you need to master Physics — for free.

Meet Phy. The world's most advanced AI helper.

1000+ Physics problems + AI help to supercharge learning.

8 AP Physics units condensed into 8 short review guides.

Proven tips, tricks, and hacks to help you score that coveted 5.

Learn Physics, from scratch, at your own pace.

Guaranteed performance boost in scores and understanding.

5 weeks for a 5. Expedited progress. Stellar Results.

1-to-1 lessons covering AP Physics from start to end.

Other 1-to-1 and group programs to accelerate Physics mastery.

What we found:

Nerd Notes

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