Q: A soccer ball is kicked at $$24\ \mathrm{m/s} at$$ $$25^\circ$$ above the horizontal. What is the horizontal distance $$d$$ from the kid to the lamppost if the ball hits the lamppost at $$3.0\ \mathrm{m}$$ above the ground?

$$d = v_{0x} t$$,\ \text{where}\ t\ \text{is found from}\ y = v_{0y} t - \dfrac{1}{2} g $$t^2$

Q: If two blocks of equal mass are connected by a rope, with one on a frictionless ramp and the other hanging vertically, what is the tension $$T in $$the rope when the system is accelerating?

$$T = m_1$ g - m_2$ g \sin \theta$$

Q: Simon swims $$100\ \mathrm{m} at$$ $$20^\circ$$ North of East, then $$200\ \mathrm{m}$$ due East, and finally $$800\ \mathrm{m}$$ due West. What is the direction of his total displacement relative to East?

$$\tan$$^{-1}$$\left(\dfrac{100 \sin 20^\circ}{100 \cos 20^\circ + 200 - 800}\right)$$ North of East

Q: A soccer ball is kicked at $$24\ \mathrm{m/s} at$$ $$25^\circ$$ above the horizontal. What is the speed of the ball just before it hits the lamppost at $$3.0\ \mathrm{m}$$ above the ground?

$$v = \sqrt{v_x^2$ + v_y^2$}$$,\ \text{where}\ v_x = v_{0x},\ v_y = v_{0y} - g t$

Question 1

A block of mass $$m_2 is $$placed on a frictionless ramp inclined at an angle $$	heta = 20^\circ to $$the horizontal. What is the correct expression for the normal force $$N$$ exerted by the ramp on the block?

Accepted Answer

$$N = m_2$ g \cos 	heta$$

Question 2

Two blocks, each of mass $$4.0\ \mathrm{kg}$$, are connected by a rope. Block 2 is on a frictionless ramp at $$20^\circ$$, and block 1 hangs vertically. If the system is released from rest, which direction will block 1 accelerate?

Accepted Answer

Block 1 will accelerate downward.

Question 3

A soccer ball is kicked with an initial speed of $$24\ \mathrm{m/s} at an $$angle of $$25^\circ$$ above the horizontal. What is the initial vertical component of the velocity?

Accepted Answer

$$24 \sin 25^\circ$$

Question 4

Given the soccer ball is kicked at $$24\ \mathrm{m/s}$$ and $$25^\circ$$ above the horizontal, what is the maximum height $$h_{max}$$ reached by the ball? (Neglect air resistance.)

Accepted Answer

$$h_{max} = \dfrac{(24 \sin 25^\$$circ)^2$$}{2g}$$

Question 5

A soccer ball is kicked and hits a lamppost at a height of $$3.0\ \mathrm{m}$$ above the ground. Which kinematic equation would you use to find the time $$t it $$takes to reach this height?

Accepted Answer

$$y = v_{0y} t - \dfrac{1}{2} g t^2$

Question 6

Simon dives underwater and swims $$100\ \mathrm{m} at an $$angle of $$20^\circ$$ North of East, then $$200\ \mathrm{m}$$ due East, and finally $$800\ \mathrm{m}$$ due West. What is the correct vector notation for Simon's total displacement $$\vec{r}_{tot}$$?

Accepted Answer

$$\vec{r}_{tot} = 100 \cos 20^\circ \hat{i} + 100 \sin 20^\circ \hat{j} + 200 \hat{i} - 800 \hat{i}$$

Question 7

If Simon's total displacement vector is $$\vec{r}_{tot} = (100 \cos 20^\circ + 200 - 800) \hat{i} + (100 \sin 20^\circ) \hat{j}$$, what is the magnitude of his displacement?

Accepted Answer

$$\sqrt{(100 \cos 20^\circ + 200 - 800)^2$ + (100 \sin 20^\$$circ)^2$$}$$

Question 8

A block of mass $$m is $$placed on a frictionless incline at angle $$	heta. $$What is the acceleration $$a of $$the block down the ramp?

Accepted Answer

$$a = g \sin 	heta$$

Question 9

A soccer ball is kicked at $$24\ \mathrm{m/s} at$$ $$25^\circ$$ above the horizontal. What is the horizontal distance $$d$$ from the kid to the lamppost if the ball hits the lamppost at $$3.0\ \mathrm{m}$$ above the ground?

Accepted Answer

$$d = v_{0x} t$$,\ 	ext{where}\ t\ 	ext{is found from}\ y = v_{0y} t - \dfrac{1}{2} g $$t^2$

Question 10

If two blocks of equal mass are connected by a rope, with one on a frictionless ramp and the other hanging vertically, what is the tension $$T in $$the rope when the system is accelerating?

Accepted Answer

$$T = m_1$ g - m_2$ g \sin 	heta$$

Question 11

Simon swims $$100\ \mathrm{m} at$$ $$20^\circ$$ North of East, then $$200\ \mathrm{m}$$ due East, and finally $$800\ \mathrm{m}$$ due West. What is the direction of his total displacement relative to East?

Accepted Answer

$$	an$$^{-1}$$\left(\dfrac{100 \sin 20^\circ}{100 \cos 20^\circ + 200 - 800}ight)$$ North of East

Question 12

A soccer ball is kicked at $$24\ \mathrm{m/s} at$$ $$25^\circ$$ above the horizontal. What is the speed of the ball just before it hits the lamppost at $$3.0\ \mathrm{m}$$ above the ground?

Accepted Answer

$$v = \sqrt{v_x^2$ + v_y^2$}$$,\ 	ext{where}\ v_x = v_{0x},\ v_y = v_{0y} - g t$

Question 13

Which of the following best describes the physical meaning of the normal force on a block resting on an inclined plane?

Accepted Answer

It is the force perpendicular to the surface that supports the block against gravity.

Question 14

If Simon's position is $$\vec{r} = (x \hat{i} + y \hat{j})$$, and his bro is at $$\vec{r}_{bro} = (x_{bro} \hat{i} + y_{bro} \hat{j})$$, what is the vector from Simon to his bro?

Accepted Answer

$$\vec{r}_{bro} - \vec{r}$$

Question 15

A block of mass $$m is $$placed on a frictionless ramp at angle $$	heta. If $$the block is connected to another block of equal mass hanging vertically, what is the net force on the system?

Accepted Answer

$$F_{net} = m g - m g \sin 	heta$$

Question 16

Which of the following is the correct method to find the magnitude of the distance between two points given by vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$|\vec{A} - \vec{B}|$$

Question 17

A soccer ball is kicked at $$24\ \mathrm{m/s} at$$ $$25^\circ$$ above the horizontal. What is the time $$t to $$reach the maximum height?

Accepted Answer

$$t = \dfrac{v_{0y}}{g}$$

Physics I: Mechanics – Sample Exam Problems and Grading Rubric

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