Q: A projectile is fired from the edge of a cliff with initial velocity components $$v_{0x} = 40.0\ \mathrm{m/s}$$ and $$v_{0y} = 75\ \mathrm{m/s}. $$The projectile lands in the sea after $$50.0\ \mathrm{s}. $$What is the height of the cliff?

$$-1.23 \times 10^4$\ \mathrm{m}$$

Q: A projectile is launched from a height $$h$$ above the ground with initial velocity $$v_0 at an $$angle $$\theta$$ above the horizontal. Which equation gives the total time of flight until it hits the ground?

$$t = \frac{v_0$ \sin \theta + \sqrt{(v_0$ \sin \$$theta)^2$$ + 2gh}}{g}$$

Q: A block of mass $$m is $$pulled across a rough horizontal surface with a constant velocity by a force $$F at an $$angle $$\theta$$ above the horizontal. What is the coefficient of kinetic friction $$\mu_k$$?

$$\mu_k = \frac{F \cos \theta}{mg}$$

Question 1

Given vectors $$\vec{A}$$ and $$\vec{B}$$ start from the origin and lie in the second and third quadrants, respectively. $$\vec{A}$$ has a magnitude of 16.0 units and forms an angle of $$42.0^\circ$$ with the negative x-axis, while $$\vec{B}$$ has a magnitude of 7.00 units and forms an angle of $$31.0^\circ$$ with the negative x-axis. If $$\vec{C} = \vec{B} - \vec{A}$$, what is the magnitude of $$\vec{C}$$?

Accepted Answer

$$9.53$$

Question 2

A boy throws a rock with an initial velocity of $$2.15\ \mathrm{m/s} at$$ $$30.0^\circ$$ above the horizontal. Neglecting air resistance, how long does it take for the rock to reach the maximum height of its trajectory?

Accepted Answer

$$0.194\ \mathrm{s}$$

Question 3

A projectile is fired from the edge of a cliff with initial velocity components $$v_{0x} = 40.0\ \mathrm{m/s}$$ and $$v_{0y} = 75\ \mathrm{m/s}. $$The projectile lands in the sea after $$50.0\ \mathrm{s}. $$What is the height of the cliff?

Accepted Answer

$$-1.23 	imes 10^4$\ \mathrm{m}$$

Question 4

Two blocks of mass $$12.0\ \mathrm{kg}$$ and $$9.0\ \mathrm{kg}$$ are placed one above the other on a horizontal table. The $$12.0\ \mathrm{kg}$$ block is held by a horizontal rope, and the $$9.0\ \mathrm{kg}$$ block is attached to a $$5.0\ \mathrm{kg}$$ block hanging vertically from a pulley. The coefficient of kinetic friction between the blocks is $$\mu_k = 0.30. If $$the $$5.0\ \mathrm{kg}$$ block accelerates downward when released, what is its acceleration?

Accepted Answer

$$3.27\ \mathrm{m/s^2$}$$

Question 5

Which of the following best describes the direction of the friction force acting between the $$12.0\ \mathrm{kg}$$ and $$9.0\ \mathrm{kg}$$ blocks in the pulley system?

Accepted Answer

Opposite to the direction of motion of the $$9.0\ \mathrm{kg}$$ block

Question 6

If the coefficient of kinetic friction between the $$12.0\ \mathrm{kg}$$ and $$9.0\ \mathrm{kg}$$ blocks were doubled, what would happen to the acceleration of the $$5.0\ \mathrm{kg}$$ block?

Accepted Answer

It would decrease

Question 7

A projectile is launched from a height $$h$$ above the ground with initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. Which equation gives the total time of flight until it hits the ground?

Accepted Answer

$$t = \frac{v_0$ \sin 	heta + \sqrt{(v_0$ \sin \$$theta)^2$$ + 2gh}}{g}$$

Question 8

A vector $$\vec{D}$$ has components $$D_x = -8.0$$ units and $$D_y = 6.0$$ units. What is the angle $$	heta$$ that $$\vec{D}$$ makes with the positive x-axis?

Accepted Answer

$$143^\circ$$

Question 9

A car travels east for $$50.0\ \mathrm{km}$$, then north for $$30.0\ \mathrm{km}$$, and finally west for $$20.0\ \mathrm{km}. $$What is the magnitude of the car's displacement from its starting point?

Accepted Answer

$$36.1\ \mathrm{km}$$

Question 10

A ball is thrown horizontally from the top of a $$45.0\ \mathrm{m}$$ high cliff with a speed of $$10.0\ \mathrm{m/s}. $$How far from the base of the cliff will the ball land?

Accepted Answer

$$30.2\ \mathrm{m}$$

Question 11

A block slides down a frictionless incline of height $$h$$ and base length $$d. $$What is the speed of the block at the bottom of the incline?

Accepted Answer

$$\sqrt{2gh}$$

Question 12

A $$2.0\ \mathrm{kg}$$ object is acted on by a force $$\vec{F} = (4.0\hat{i} + 3.0\hat{j})\ \mathrm{N}. $$What is the magnitude of the object's acceleration?

Accepted Answer

$$5.0\ \mathrm{m/s^2$}$$

Question 13

A block of mass $$m is $$pulled across a rough horizontal surface with a constant velocity by a force $$F at an $$angle $$	heta$$ above the horizontal. What is the coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$\mu_k = \frac{F \cos 	heta}{mg}$$

Question 14

A $$10.0\ \mathrm{kg}$$ box is at rest on a horizontal surface. The coefficient of static friction is $$0.40. $$What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$39.2\ \mathrm{N}$$

Question 15

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates on a frictionless surface. If the amplitude of oscillation is $$A$$, what is the maximum speed of the block?

Accepted Answer

$$A \sqrt{\frac{k}{m}}$$

Physics with Calculus: Step-by-Step Guidance for Exam Problems

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