Q: A motorized flying toy is attached to a string of length $$L$$ and moves in a horizontal circle, making a constant angle $$\theta$$ with the vertical. If it takes $$T$$ seconds to complete one revolution, what is the magnitude of the radial acceleration?

$$a_r = \frac{4\pi^2$ L \sin\theta}{T^2$}$$

Q: A helicopter flying at height $$h at $$constant horizontal speed $$v_h is to $$release a package so that it lands in a car traveling at constant speed $$v_c. At $$what angle $$\theta to $$the horizontal should the car be in the helicopter’s sights when the package is released?

$$\theta = \arccos\left(\frac{v_c}{v_h}\right)$$

Q: A projectile is launched from the ground with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the maximum height reached by the projectile?

$$H = \frac{v_0$^2 \sin^2$\theta}{2g}$$

Question 1

A salmon swims upstream against a current flowing south at speed $$v. $$The salmon swims at speed $$v\sqrt{2} in a $$direction $$45^\circ$$ north of east. What is the velocity of the salmon with respect to the ground? (Let east be the $$+x$$ direction and north be the $$+y$$ direction.)

Accepted Answer

$$v\hat{i}$$

Question 2

Which of the following statements is FALSE?

Accepted Answer

If you are given an object's speed, you can definitely determine its velocity.

Question 3

Given any two vectors, which statement is correct?

Accepted Answer

The sum of the two vectors cannot be perpendicular to both vectors.

Question 4

You toss a ball into the air at an initial angle $$45^\circ$$ from the horizontal. At what point in the ball’s trajectory does the ball have the smallest speed? Neglect air resistance.

Accepted Answer

At the highest point in its flight

Question 5

The acceleration vector of a particle in uniform circular motion:

Accepted Answer

Points toward the center of the circle.

Question 6

A motorized flying toy is attached to a string of length $$L$$ and moves in a horizontal circle, making a constant angle $$	heta$$ with the vertical. If it takes $$T$$ seconds to complete one revolution, what is the magnitude of the radial acceleration?

Accepted Answer

$$a_r = \frac{4\pi^2$ L \sin	heta}{T^2$}$$

Question 7

A small object begins a free-fall from rest from a height $$H$$ above the ground. At the same time, a second object is launched vertically upward from the ground with initial velocity $$v_0. At $$what height above the ground will the two objects first meet?

Accepted Answer

$$H - \frac{v_0$^2}{2g}$$

Question 8

A rocket follows the trajectory $$\vec{r}(t) = bt^2$\hat{i} + ct^3$\hat{j}$$, where $$b$$ and $$c$$ are positive constants. At what time will the acceleration vector point exactly $$45^\circ$$ between the $$x$$ and $$y$$ axes?

Accepted Answer

$$t = \sqrt{\frac{b}{6c}}$$

Question 9

A helicopter flying at height $$h at $$constant horizontal speed $$v_h is to $$release a package so that it lands in a car traveling at constant speed $$v_c. At $$what angle $$	heta to $$the horizontal should the car be in the helicopter’s sights when the package is released?

Accepted Answer

$$	heta = \arccos\left(\frac{v_c}{v_h}ight)$$

Question 10

A car is moving at constant speed $$v$$ around a circular track of radius $$R. $$What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{v^2$}{R}$$

Question 11

A projectile is launched from the ground with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the maximum height reached by the projectile?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$	heta}{2g}$$

Question 12

A plane is flying with velocity $$\vec{v}_p$$ relative to the air, and the wind is blowing with velocity $$\vec{v}_w$$ relative to the ground. What is the velocity of the plane relative to the ground?

Accepted Answer

$$\vec{v}_p + \vec{v}_w$$

Question 13

A ball is thrown straight up with initial velocity $$v_0. $$How long does it take to return to the thrower's hand?

Accepted Answer

$$t = \frac{2v_0}{g}$$

Question 14

A car accelerates from rest at a constant rate $$a$$ for time $$t. $$What is the distance traveled?

Accepted Answer

$$d = \frac{1}{2} a t^2$

Physics 10310 Exam #1 Study Guidance

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드