Q: A skier starts from rest and accelerates down a 360 m slope, dropping a vertical distance of 170 m. Assuming no friction, what is the fastest speed the skier could achieve at the end of the run? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$v = \sqrt{2g\Delta y} = \sqrt{2 \times 9.8 \times 170} = 58\ \mathrm{m/s}$$

Q: A ball is thrown at an angle $$\theta$$ with initial speed $$v_i. $$What is the time to reach maximum height?

$$t = \frac{v_i \sin \theta}{g}$$

Q: A vector has $$A_x = -8$$ and $$A_y = 6. $$What is the angle it makes with the positive x-axis?

$$\theta = \arctan\left(\frac{A_y}{A_x}\right) = \arctan\left(\frac{6}{-8}\right)$$

Q: A crate slides down a frictionless incline of length $$L$$ and angle $$\theta. $$What is the time to reach the bottom?

$$t = \sqrt{\frac{2L}{g \sin \theta}}$$

Question 1

A skier starts from rest and accelerates down a 360 m slope, dropping a vertical distance of 170 m. Assuming no friction, what is the fastest speed the skier could achieve at the end of the run? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v = \sqrt{2g\Delta y} = \sqrt{2 	imes 9.8 	imes 170} = 58\ \mathrm{m/s}$$

Question 2

A vector has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of the vector?

Accepted Answer

$$A = \sqrt{A_x^2$ + A_y^2$} = \sqrt{3^2$ + 4^2$} = 5$$

Question 3

A projectile is launched with an initial speed $$v_i at an $$angle $$	heta$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$v_{iy} = v_i \sin 	heta$$

Question 4

A car rounds a curve of radius $$r at $$constant speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 5

A ball is thrown horizontally from a cliff with speed $$v_0. $$Neglecting air resistance, what is the horizontal acceleration of the ball?

Accepted Answer

$$a_x = 0$$

Question 6

A crate slides down a frictionless ramp inclined at angle $$	heta to $$the horizontal. What is the acceleration of the crate along the ramp?

Accepted Answer

$$a = g \sin 	heta$$

Question 7

A runner moves at $$5\ \mathrm{m/s}$$ relative to the ground. A car moves at $$15\ \mathrm{m/s} in $$the same direction. What is the velocity of the runner relative to the car?

Accepted Answer

$$v_{runner,car} = 5 - 15 = -10\ \mathrm{m/s}$$

Question 8

A projectile is launched at $$30^\circ$$ above the horizontal with speed $$v_i. $$What is the horizontal component of its velocity?

Accepted Answer

$$v_{ix} = v_i \cos 30^\circ$$

Question 9

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal and vertical motions are independent except for sharing the same time of flight.

Question 10

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the x-axis. Which equation gives the y-component of $$\vec{A}$$?

Accepted Answer

$$A_y = A \sin 	heta$$

Question 11

A car moves in a circle at constant speed. Which of the following is true?

Accepted Answer

The car is accelerating because its velocity direction is changing.

Question 12

A ball is thrown at an angle $$	heta$$ with initial speed $$v_i. $$What is the time to reach maximum height?

Accepted Answer

$$t = \frac{v_i \sin 	heta}{g}$$

Question 13

A vector has $$A_x = -8$$ and $$A_y = 6. $$What is the angle it makes with the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{A_y}{A_x}ight) = \arctan\left(\frac{6}{-8}ight)$$

Question 14

A crate slides down a frictionless incline of length $$L$$ and angle $$	heta. $$What is the time to reach the bottom?

Accepted Answer

$$t = \sqrt{\frac{2L}{g \sin 	heta}}$$

Question 15

A projectile is launched horizontally from a height $$h. $$How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Analyzing Motion on an Inclined Plane: Maximum Speed of a Skier

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