Q: A projectile is launched from the ground at an angle $$ heta$$ with initial speed $$v_0. $$Which equation gives the time of flight if it lands at the same height?

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

Q: A cannonball is launched at $$60^ ext{o}$$ from a height of $$0.50 m $$and hits a building $$30 m $$away. What is the equation for the $$x-$$component of its position as a function of time?

$$x(t) = v_0$ \cos\theta \cdot t$$

Q: A rocket accelerates upward at $$2.50 m/s$^2$$ until it reaches $$200 m$$, then coasts upward. What is the speed of the rocket when it runs out of fuel?

$$v = 43.0 m/s$$ $$+ \sqrt{2 \times 2.50 \times 200}$$

Q: A projectile is launched from a height $$h$$ above the ground. What is the equation for its vertical position as a function of time?

$$y(t) = h + v_0$ \sin\theta \cdot t - \frac{1}{2}gt^2$

Q: A block of mass $$m is $$pulled up a frictionless incline at angle $$\theta by a $$force $$F. $$What is the net force acting on the block?

$$F_{net} = F - mg \sin\theta$$

Question 1

A vehicle moves along a straight road. Its position as a function of time is given by $$x(t) = 2t^2$ + 3t. $$What is the average velocity of the vehicle between $$t = 0 s $$and $$t = 5 s$$?

Accepted Answer

$$v_{avg} = 15 m/s$$

Question 2

A cannonball is launched from a height of $$0.50 m $$above the ground with a speed of $$25.0 m/s at an $$angle of $$60^	ext{o}$$ above the horizontal. What is the initial vertical component of the velocity?

Accepted Answer

$$v_{0y} = 21.7 m/s$$

Question 3

A truck moves at $$5.00 m/s in $$the positive $$x-$$direction. A student throws a ball upward and catches it $$20.0 m $$farther down the road. Neglecting air resistance, how long is the ball in the air?

Accepted Answer

$$t = 4.00 s$$

Question 4

Two blocks, $$m_1 = 2.00$ kg and m_2$ = 1.00 kg$$, are connected on a frictionless incline at $$25^	ext{o}$$ with a force $$F = 40.0 N $$pulling $$m_1 up $$the incline. What is the acceleration of the blocks?

Accepted Answer

$$a = 14.2 m/s$^2$$

Question 5

Three masses are connected by strings over a frictionless pulley: $$m_1 = 4.50$ kg$$, $$m_2 = 3.00$ kg$$, $$m_3 = 3.00$ kg. $$What is the acceleration of $$m_1 if$$ $$m_3$ hangs freely?

Accepted Answer

$$a = 1.96 m/s$^2$$

Question 6

A model rocket is launched straight up with an initial speed of $$43.0 m/s $$and accelerates upward at $$2.50 m/s$^2$$ until it reaches $$200 m $$altitude. What is the maximum height reached by the rocket?

Accepted Answer

$$h_{max} = 278 m$$

Question 7

A projectile is launched from the ground at an angle $$	heta$$ with initial speed $$v_0. $$Which equation gives the time of flight if it lands at the same height?

Accepted Answer

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

Question 8

A student throws a ball upward from a moving truck. In the ground frame, what is the initial velocity of the ball if the student throws it straight up at $$10.0 m/s $$and the truck moves at $$5.00 m/s$$?

Accepted Answer

$$\vec{v}_0 = 5.00\hat{i} + 10.0\hat{j} m/s$$

Question 9

Two vehicles travel along a straight road. Vehicle 1 moves at constant velocity, while Vehicle 2 starts behind and moves faster. If Vehicle 2 overtakes Vehicle 1 after $$t$$ seconds, which equation relates their velocities and initial positions?

Accepted Answer

$$x_{1,0} + v_1$ t = x_{2,0} + v_2$ t$$

Question 10

A cannonball is launched at $$60^	ext{o}$$ from a height of $$0.50 m $$and hits a building $$30 m $$away. What is the equation for the $$x-$$component of its position as a function of time?

Accepted Answer

$$x(t) = v_0$ \cos	heta \cdot t$$

Question 11

A block of mass $$m$$ slides down a frictionless incline of angle $$	heta. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin	heta$$

Question 12

A rocket accelerates upward at $$2.50 m/s$^2$$ until it reaches $$200 m$$, then coasts upward. What is the speed of the rocket when it runs out of fuel?

Accepted Answer

$$v = 43.0 m/s$$ $$+ \sqrt{2 	imes 2.50 	imes 200}$$

Question 13

Three masses are connected by strings over a pulley. If $$m_1 = 4.50$ kg, m_2$ = 3.00 kg$, m_3$ = 3.00 kg$$, and the system is released from rest, which mass will accelerate downward?

Accepted Answer

$$m_3$$

Question 14

A block is pulled up a frictionless incline by a force $$F$$ parallel to the incline. What is the tension in the rope connecting two blocks of masses $$m_1$$ and $$m_2$$?

Accepted Answer

$$T = m_2$ a$$

Question 15

A projectile is launched from a height $$h$$ above the ground. What is the equation for its vertical position as a function of time?

Accepted Answer

$$y(t) = h + v_0$ \sin	heta \cdot t - \frac{1}{2}gt^2$

Question 16

A rocket is launched upward and reaches its maximum height after $$t$$ seconds. What is the speed of the rocket when it hits the ground?

Accepted Answer

$$v = \sqrt{v_0$^2 + 2gh}$$

Question 17

A block of mass $$m is $$pulled up a frictionless incline at angle $$	heta by a $$force $$F. $$What is the net force acting on the block?

Accepted Answer

$$F_{net} = F - mg \sin	heta$$

Question 18

A student throws a ball upward from a moving truck. In the truck's frame, the ball is thrown straight up at $$10.0 m/s. $$What is the ball's initial velocity in the ground frame?

Accepted Answer

$$\vec{v}_0 = 5.00\hat{i} + 10.0\hat{j} m/s$$

Kinematics and Dynamics: College Physics Exam Study Guide

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