Q: A projectile is launched at an initial speed $$v_0$$ and angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the formula for its maximum height?

$$h_{max} = \dfrac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A grasshopper jumps a distance of 0.76 m at the optimal angle for maximum range. What is the minimum speed required for the jump? (Use $$g = 9.8 m/s$^2)$$

$$v_0$$ = \sqrt{0.76 \times 9.8 / \sin(2 \times 45^\circ)}$$

Q: A projectile is launched from ground level with initial speed $$v_0 at $$angle $$\theta. $$What is the formula for its range?

$$R = \dfrac{v_0$^2 \sin(2\theta)}{g}$$

Q: A flock of geese flies 4.0 km east in 4.5 minutes, then turns 40° north of east and flies 3.0 km in 7.0 minutes. What is the magnitude of their displacement from the starting point?

$$\sqrt{4.0^2$ + 3.0^2$ + 2 \times 4.0 \times 3.0 \cos(40^\circ)}$$

Question 1

A cheetah runs with a velocity vector of magnitude 30 m/s at an angle of 20° above the horizontal. What are the x- and y-components of its velocity?

Accepted Answer

$$v_x = 30 \cos(20^\circ)$$, $$v_y = 30 \sin(20^\circ)$$

Question 2

Which rule allows you to add two vectors graphically by sliding the tail of one vector to the tip of the other?

Accepted Answer

Tip-to-tail rule

Question 3

A projectile is launched at an initial speed $$v_0$$ and angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the formula for its maximum height?

Accepted Answer

$$h_{max} = \dfrac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 4

A tranquilizer dart is shot at a monkey hanging from a tree. If the monkey lets go and drops at the instant the dart is fired, where should the dart be aimed to hit the monkey?

Accepted Answer

Directly at the monkey

Question 5

Which of the following statements about projectile motion is TRUE (neglecting air resistance)?

Accepted Answer

The vertical acceleration is constant and equal to $$-g.$$

Question 6

A football is kicked with an initial speed $$v_0 at an $$angle $$	heta$$ for maximum range. What is the optimal launch angle?

Accepted Answer

$$45^\circ$$

Question 7

A bullet is fired horizontally at a target 50 m away and hits the target in 0.2 s. What was the bullet's initial speed?

Accepted Answer

$$v = \dfrac{50}{0.2} = 250 m/s$$

Question 8

A grasshopper jumps a distance of 0.76 m at the optimal angle for maximum range. What is the minimum speed required for the jump? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$v_0$$ = \sqrt{0.76 	imes 9.8 / \sin(2 	imes 45^\circ)}$$

Question 9

If a vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4$$, what is its magnitude?

Accepted Answer

$$|\vec{A}| = \sqrt{3^2$ + 4^2$} = 5$$

Question 10

A projectile is launched from ground level with initial speed $$v_0 at $$angle $$	heta. $$What is the formula for its range?

Accepted Answer

$$R = \dfrac{v_0$^2 \sin(2	heta)}{g}$$

Question 11

A car runs out of gas while traveling up a 5° slope at 30 m/s. Neglecting friction, how far will it travel up the slope before stopping? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$d = \dfrac{v^2$}{2g \sin(5^\circ)}$$

Question 12

Which of the following is NOT a property of a vector?

Accepted Answer

Its magnitude can be negative.

Question 13

A flock of geese flies 4.0 km east in 4.5 minutes, then turns 40° north of east and flies 3.0 km in 7.0 minutes. What is the magnitude of their displacement from the starting point?

Accepted Answer

$$\sqrt{4.0^2$ + 3.0^2$ + 2 	imes 4.0 	imes 3.0 \cos(40^\circ)}$$

Question 14

Which of the following best describes the direction of the acceleration vector for a projectile at the highest point of its trajectory?

Accepted Answer

Downward

Question 15

If you multiply a vector by a negative scalar, what happens to the vector?

Accepted Answer

Its direction reverses, but magnitude stays the same.

Question 16

A projectile is launched horizontally from a height $$h. $$What is the time to hit the ground?

Accepted Answer

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

Question 17

Which of the following is the correct formula for the velocity vector of a projectile at time $$t$$ after launch at angle $$	heta$$ and speed $$v_0$$?

Accepted Answer

$$\vec{v}(t) = (v_0$ \cos 	heta, v_0$ \sin 	heta - gt)$$

Question 18

A ball is dropped and another is fired horizontally from the same height. Neglecting air resistance, which hits the ground first?

Accepted Answer

Both hit at the same time

Vectors and Motion in Two Dimensions: Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드