Q: A block of mass $$m_1 is on an $$incline of angle $$\theta. If a $$force $$F$$ pulls the block up the incline and the tension in the rope is $$T$$, which equation correctly represents the force balance for $$m_1$$ along the incline?

$$F - m_1$ g \sin\theta - T = m_1$ a$$

Q: A student throws a ball straight up from a moving truck. In the ground frame, what is the initial velocity of the ball?

$$\vec{v}_{\text{ball, ground}} = \vec{v}_{\text{truck}} + \vec{v}_{\text{ball, truck}}$$

Q: For a projectile launched at an angle $$\theta$$ with initial speed $$v_0$$, which equation gives the horizontal range if it lands at the same height it was launched?

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

Q: A block of mass $$m_2 is $$connected to $$m_1 on an $$incline by a rope. If the acceleration of the system is $$a$$, what is the tension $$T in $$the rope connecting the two blocks?

$$T = m_2$ (a + g \sin\theta)$$

Q: A truck moves at $$5.00\ \mathrm{m/s}$$ and a student throws a ball straight up with respect to the truck. What is the velocity of the ball relative to the ground?

$$\vec{v}_{\text{ball, ground}} = 5.00\ \mathrm{m/s}\ \hat{i} + 19.6\ \mathrm{m/s}\ \hat{j}$$

Question 1

A vehicle moves along the x-axis with a constant velocity of $$0.60\ \mathrm{m/s}$$ for $$5.00\ \mathrm{s}$$, starting from $$x=0. $$What is the total displacement of the vehicle after $$5.00\ \mathrm{s}$$?

Accepted Answer

$$3.00\ \mathrm{m}$$

Question 2

Two vehicles are moving along a straight road. Vehicle 1 moves at $$0.60\ \mathrm{m/s}$$ and Vehicle 2 at $$2.00\ \mathrm{m/s}. If $$Vehicle 2 starts $$5.00\ \mathrm{m}$$ behind Vehicle 1, how long will it take for Vehicle 2 to overtake Vehicle 1?

Accepted Answer

$$3.57\ \mathrm{s}$$

Question 3

A cannonball is launched at $$25.0\ \mathrm{m/s} at an $$angle of $$60^\circ$$ above the horizontal from a height of $$0.50\ \mathrm{m}. $$How long does it take for the cannonball to hit a building $$30.0\ \mathrm{m}$$ away?

Accepted Answer

$$2.40\ \mathrm{s}$$

Question 4

A truck moves at $$5.00\ \mathrm{m/s} in $$the positive x-direction. A student throws a ball straight up from the back of the truck and catches it $$20.0\ \mathrm{m}$$ down the road. Neglecting air resistance, how long is the ball in the air?

Accepted Answer

$$4.00\ \mathrm{s}$$

Question 5

A block of mass $$m_1 = 2.00$$\ \mathrm{kg}$$ is connected by a rope to a second block of mass m_2$ = 1.00\ \mathrm{kg} on an $$incline of $$25.0^\circ. A $$force $$F = 40.0\ \mathrm{N}$$ pulls $$m_1 up $$the incline. What is the acceleration of the system? (Neglect friction.)

Accepted Answer

$$9.16\ \mathrm{m/s^2$}$$

Question 6

Three objects $$m_1 = 4.50$$\ \mathrm{kg}$$, m_2$ = 3.00\ \mathrm{kg}$$, and $$m_3 = 3.00$$\ \mathrm{kg}$$ are connected by strings over a frictionless pulley. What is the acceleration of the system?

Accepted Answer

$$1.40\ \mathrm{m/s^2$}$$

Question 7

A rocket is launched straight upward with an initial speed of $$43.0\ \mathrm{m/s}$$ and a constant upward acceleration of $$2.50\ \mathrm{m/s^2$}$$ until it runs out of fuel at $$200\ \mathrm{m}. $$What is the maximum height reached by the rocket?

Accepted Answer

$$315\ \mathrm{m}$$

Question 8

A cannonball is launched at $$25.0\ \mathrm{m/s} at$$ $$60^\circ$$ above the horizontal from a height of $$0.50\ \mathrm{m}. $$What is the vertical component of the velocity just before it hits the building $$30.0\ \mathrm{m}$$ away?

Accepted Answer

$$-1.89\ \mathrm{m/s}$$

Question 9

A block of mass $$m_1 is on an $$incline of angle $$	heta. If a $$force $$F$$ pulls the block up the incline and the tension in the rope is $$T$$, which equation correctly represents the force balance for $$m_1$$ along the incline?

Accepted Answer

$$F - m_1$ g \sin	heta - T = m_1$ a$$

Question 10

A student throws a ball straight up from a moving truck. In the ground frame, what is the initial velocity of the ball?

Accepted Answer

$$\vec{v}_{	ext{ball, ground}} = \vec{v}_{	ext{truck}} + \vec{v}_{	ext{ball, truck}}$$

Question 11

A rocket accelerates upward at $$2.50\ \mathrm{m/s^2$}$$ until it reaches $$200\ \mathrm{m}$$, then coasts upward. How long is the rocket in the air before it returns to the ground?

Accepted Answer

$$18.0\ \mathrm{s}$$

Question 12

For a projectile launched at an angle $$	heta$$ with initial speed $$v_0$$, which equation gives the horizontal range if it lands at the same height it was launched?

Accepted Answer

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

Question 13

Three masses $$m_1$$, $$m_2$$, and $$m_3$$ are connected as shown in a pulley system. If $$m_1 = 4.50$$\ \mathrm{kg}$$, m_2$ = 3.00\ \mathrm{kg}$$, and $$m_3 = 3.00$$\ \mathrm{kg}$$, what is the tension in the string between m_1$ and m_2$?

Accepted Answer

$$50.5\ \mathrm{N}$$

Question 14

A cannonball is launched at $$25.0\ \mathrm{m/s} at$$ $$60^\circ$$ from a height of $$0.50\ \mathrm{m}. $$What is the speed and orientation of the ball when it hits the building $$30.0\ \mathrm{m}$$ away?

Accepted Answer

$$12.6\ \mathrm{m/s} at$$ $$-8.6^\circ$$ below the horizontal

Question 15

A block of mass $$m_2 is $$connected to $$m_1 on an $$incline by a rope. If the acceleration of the system is $$a$$, what is the tension $$T in $$the rope connecting the two blocks?

Accepted Answer

$$T = m_2$ (a + g \sin	heta)$$

Question 16

A rocket is launched upward with an initial speed of $$43.0\ \mathrm{m/s}$$ and an acceleration of $$2.50\ \mathrm{m/s^2$}$$ until it runs out of fuel at $$200\ \mathrm{m}. $$What is the speed of the rocket when it hits the ground?

Accepted Answer

$$62.3\ \mathrm{m/s}$$ downward

Question 17

A truck moves at $$5.00\ \mathrm{m/s}$$ and a student throws a ball straight up with respect to the truck. What is the velocity of the ball relative to the ground?

Accepted Answer

$$\vec{v}_{	ext{ball, ground}} = 5.00\ \mathrm{m/s}\ \hat{i} + 19.6\ \mathrm{m/s}\ \hat{j}$$

Question 18

A block of mass $$m_1 is $$pulled up an incline by a force $$F at $$angle $$	heta. If $$friction is neglected, what is the net force on $$m_1$$ along the incline?

Accepted Answer

$$F - m_1$ g \sin	heta$$

Question 19

A projectile is launched horizontally from a height $$h$$ with speed $$v_0. $$What is the time to hit the ground?

Accepted Answer

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

Kinematics and Dynamics: Exam Study Guide with Worked Examples

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