CP Vectors and Projectile Practice for Test

Zoe, Rohan, and Jackson are discussing vectors in their math class. Rohan asks, "What is a vector?"

• A vector is a mathematical object that has both magnitude and direction.

• A vector is a mathematical object that has only magnitude.

• A vector is a mathematical object that has only direction.

• A vector is a mathematical object that has neither magnitude nor direction.

A plane travels at a velocity of 67 m/s North into a crosswind blowing at 67 m/s east. What is the actual velocity of the plane?

• 67 m/s

• 94.8 m/s

• 134 m/s

• 47.3 m/s

Answer explanation

To find the actual velocity, use the Pythagorean theorem: \(v = \sqrt{(67^2 + 67^2)} = \sqrt{(4489 + 4489)} = \sqrt{8978} \approx 94.8 \text{ m/s}\). Thus, the correct answer is 94.8 m/s.

Tags

NGSS.MS-PS2-2

A boat wants to go directly across a river to the northern side. The river is flowing east at 40 m/s. What will be the boat's actual velocity if it tries to go across the river at 50 m/s north?

• 30 m/s

• 40 m/s

• 50 m/s

• 64 m/s

Answer explanation

The boat's velocity north is 50 m/s, and the river's current east is 40 m/s. Using the Pythagorean theorem, the resultant velocity is √(50² + 40²) = √(2500 + 1600) = √4100 ≈ 64 m/s.

A jogger runs 100m East and then 50m North. What is the resulting displacement of the jogger?

• 100m

• 50m

• 111.8m

• 150m

Answer explanation

The jogger's displacement can be calculated using the Pythagorean theorem. The eastward distance is 100m and the northward distance is 50m. Displacement = √(100² + 50²) = √(10000 + 2500) = √12500 ≈ 111.8m.

A car applies a 400 N force at 0 degrees to move forward and simultaneously experiences a 100 N force of air resistance at 180 degrees. Neglecting other frictions, what is the net force acting on the car?

• 300 N forward

• 500 N forward

• 300 N backward

• 500 N backward

Answer explanation

The car experiences a forward force of 400 N and a backward force of 100 N. The net force is 400 N - 100 N = 300 N forward, making the correct answer 300 N forward.

Tags

NGSS.HS-PS2-1

A cannon fires a projectile at an angle of 45 degrees to the horizontal with an initial speed of 100 m/s. What is the horizontal component of the projectile's initial velocity?

• 70.7 m/s

• 50 m/s

• 100 m/s

• 35.4 m/s

Answer explanation

To find the horizontal component of the initial velocity, use the formula: Vx = V * cos(θ). Here, V = 100 m/s and θ = 45°. Thus, Vx = 100 * cos(45°) = 100 * 0.707 = 70.7 m/s, which is the correct answer.

An object simultaneously moving east at 3 m/s and north at 4 m/s has a resultant direction of:

• 37^o

• 42^o

• 49^o

• 53^o

Answer explanation

To find the resultant direction, use the tangent function: tan(θ) = opposite/adjacent = 4/3. Thus, θ = arctan(4/3) ≈ 53°. Therefore, the correct answer is 53°.

The _______ of two or more vectors is the sum of the vectors.

• components

• scalar

• resultant

• magnitude

Answer explanation

The resultant of two or more vectors is the vector sum of those vectors. It represents the combined effect of the vectors, making 'resultant' the correct choice in this context.

A plane traveling 300 m/s south is hit by a crosswind blowing 50 m/s west. What is the plane's resultant velocity?

• 350 m/s

• 250 m/s

• 6 m/s

• 304 m/s

Answer explanation

To find the resultant velocity, use the Pythagorean theorem: \( v = \sqrt{(300^2 + 50^2)} = \sqrt{(90000 + 2500)} = \sqrt{92500} \approx 304 \, m/s \). Thus, the correct answer is 304 m/s.

What is the magnitude of the vector?

• 2.24

• 10

• 3.9

• 15

• 5

Tags

NGSS.HS-PS2-4

NGSS.HS-PS3-5