Question 1

A woman walks inside a train at $$1.0\ \mathrm{m/s}$$ relative to the train, which itself moves at $$3.0\ \mathrm{m/s}$$ relative to the ground. If her direction of walking is perpendicular to the train's motion, what is her speed relative to the ground?

Accepted Answer

$$3.2\ \mathrm{m/s}$$

Question 2

A cyclist rides parallel to a train track at $$3.0\ \mathrm{m/s}$$ while a woman walks inside the train at $$1.0\ \mathrm{m/s}$$ perpendicular to the train's motion. What is the angle between the woman's velocity relative to the cyclist and the direction of the train's motion?

Accepted Answer

$$18^\circ$$

Question 3

A plane flies north at $$240\ \mathrm{km/h}$$ relative to the air, and the wind blows east at $$100\ \mathrm{km/h}. $$What is the plane's speed relative to the ground?

Accepted Answer

$$260.8\ \mathrm{km/h}$$

Question 4

Which equation correctly expresses the velocity of an object (W) relative to the ground (G), if it is moving inside a train (T) that is itself moving relative to the ground?

Accepted Answer

$$v_{W/G} = v_{W/T} + v_{T/G}$$

Question 5

A ball is thrown with an initial velocity of $$10\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$5.0\ \mathrm{m/s}$$

Question 6

Given the position vector $$\vec{r}(t) = (x(t), y(t))$$, how do you calculate the instantaneous velocity vector $$\vec{v}(t)$$?

Accepted Answer

$$\vec{v}(t) = \frac{d\vec{r}}{dt}$$

Question 7

A boat heads directly across a river at $$5\ \mathrm{m/s}$$ relative to the water. The river flows at $$3\ \mathrm{m/s}$$ downstream. What is the boat's speed relative to the ground?

Accepted Answer

$$5.8\ \mathrm{m/s}$$

Question 8

If $$\vec{v}_{A/B} = -\vec{v}_{B/A}$$, what does this mean in the context of relative velocity?

Accepted Answer

The velocity of A relative to B is equal in magnitude and opposite in direction to the velocity of B relative to A.

Question 9

A projectile is launched from the ground with velocity components $$v_x = 6\ \mathrm{m/s}$$ and $$v_y = 8\ \mathrm{m/s}. $$What is the magnitude of its initial velocity?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 10

Which of the following best describes the instantaneous velocity vector of a particle moving in two dimensions?

Accepted Answer

It is always tangent to the path of the particle.

Question 11

A car travels $$100\ \mathrm{m}$$ east in $$20\ \mathrm{s}$$, then $$100\ \mathrm{m}$$ north in $$20\ \mathrm{s}. $$What is the magnitude of its average velocity over the $$40\ \mathrm{s}$$?

Accepted Answer

$$3.54\ \mathrm{m/s}$$

Question 12

A plane must fly due north but there is a wind blowing east. If the plane's airspeed is $$240\ \mathrm{km/h}$$ and the wind speed is $$100\ \mathrm{km/h}$$, at what angle west of north should the pilot head?

Accepted Answer

$$23.6^\circ$$

Question 13

Which of the following is the correct formula for average acceleration in vector form?

Accepted Answer

$$\vec{a}_{av} = \frac{\Delta \vec{v}}{\Delta t}$$

Question 14

A person walks $$4\ \mathrm{km}$$ east and then $$3\ \mathrm{km}$$ north. What is the magnitude of their displacement?

Accepted Answer

$$5\ \mathrm{km}$$

Question 15

If $$\vec{r}_1 = (2, 3)$$ and $$\vec{r}_2 = (5, 7)$$, what is the displacement vector $$\Delta \vec{r}$$?

Accepted Answer

$$(3, 4)$$

Relative Velocity and 2-Dimensional Kinematics: Study Notes for Physics with Calculus

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