Q: A projectile is launched with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for its maximum height (neglecting air resistance)?

$$\dfrac{v_0$^2 \sin^2$\theta}{2g}$$

Q: A $$3.5\ \mathrm{kg}$$ box is being pulled along a horizontal smooth surface. The pulling force is $$24\ \mathrm{N}$$ directed at an angle of $$22^\circ$$ above the horizontal. What is the normal force on the box?

$$3.5 \times 9.8 - 24\sin22^\circ$$

Q: A cat leaps to try to catch a bird. If the cat's jump was at $$40^\circ$$ off the ground and its initial velocity was $$2.3\ \mathrm{m/s}$$, what is the highest point of its trajectory, neglecting air resistance?

$$\dfrac{(2.3\sin40^\$$circ)^2$$}{2\times9.8}$$

Q: A $$10.0\ \mathrm{kg}$$ picture is held in place by two wires, one hanging at $$50^\circ to $$the left of the vertical and the second one at $$50^\circ to $$the right of the vertical. What is the tension in the first wire?

$$\dfrac{10.0 \times 9.8}{2\cos50^\circ}$$

Question 1

A soccer ball is kicked horizontally from a cliff 20 m above the ground with an initial speed of 10 m/s. Neglecting air resistance, how far from the base of the cliff does the ball land? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$14.3\ \mathrm{m}$$

Question 2

A car of mass $$1200\ \mathrm{kg}$$ accelerates uniformly from $$0 to$$ $$27.0\ \mathrm{m/s} in$$ $$10.0\ \mathrm{s}. $$What is the magnitude of the net force required?

Accepted Answer

$$3240\ \mathrm{N}$$

Question 3

A projectile is launched with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for its maximum height (neglecting air resistance)?

Accepted Answer

$$\dfrac{v_0$^2 \sin^2$	heta}{2g}$$

Question 4

A block of mass $$5\ \mathrm{kg} is $$pulled on a horizontal frictionless surface by a force of $$10\ \mathrm{N} at an $$angle of $$35^\circ$$ above the horizontal. What is the magnitude of the normal force exerted on the block?

Accepted Answer

$$49\ \mathrm{N} - 10\sin35^\circ$$

Question 5

A velocity vector has components $$36\ \mathrm{m/s}$$ westward and $$22\ \mathrm{m/s}$$ northward. What is the magnitude of this vector?

Accepted Answer

$$\sqrt{36^2$ + 22^2$}$$

Question 6

A rock is thrown from the upper edge of a tall cliff at some angle above the horizontal. It reaches its highest point and starts falling down. Which statement is true about the rock's velocity at its highest point?

Accepted Answer

Its vertical velocity component is zero.

Question 7

A traffic light weighing $$100\ \mathrm{N} is $$suspended by two ropes at equal angles from the vertical. What is the tension in each rope?

Accepted Answer

$$\dfrac{100}{2\cos	heta}$$

Question 8

An astronaut weighs $$741\ \mathrm{N} on $$Earth ($$g = 9.80\ \mathrm{m/s^2$}) $$and $$532\ \mathrm{N} on $$another planet. What is the acceleration due to gravity on that planet?

Accepted Answer

$$7.04\ \mathrm{m/s^2$}$$

Question 9

A $$3.5\ \mathrm{kg}$$ box is being pulled along a horizontal smooth surface. The pulling force is $$24\ \mathrm{N}$$ directed at an angle of $$22^\circ$$ above the horizontal. What is the normal force on the box?

Accepted Answer

$$3.5 	imes 9.8 - 24\sin22^\circ$$

Question 10

A cat leaps to try to catch a bird. If the cat's jump was at $$40^\circ$$ off the ground and its initial velocity was $$2.3\ \mathrm{m/s}$$, what is the highest point of its trajectory, neglecting air resistance?

Accepted Answer

$$\dfrac{(2.3\sin40^\$$circ)^2$$}{2	imes9.8}$$

Question 11

A block lies on a horizontal frictionless surface. A horizontal force of $$100\ \mathrm{N} is $$applied to the block, giving it an acceleration of $$3.33\ \mathrm{m/s^2$}. $$What is the mass of the block?

Accepted Answer

$$30\ \mathrm{kg}$$

Question 12

A displacement vector is $$3.40\ \mathrm{m} in $$length and is directed $$60^\circ$$ south of east. What are its components?

Accepted Answer

$$x = 3.40\cos60^\circ$$, $$y = -3.40\sin60^\circ$$

Question 13

Which of the following is a vector quantity?

Accepted Answer

The velocity of a car

Question 14

For general projectile motion with no air resistance, the horizontal component of a projectile's velocity:

Accepted Answer

remains constant

Question 15

A student throws a rock horizontally from a bridge with a velocity of $$10\ \mathrm{m/s}. $$The rock falls $$20\ \mathrm{m} to $$the water below. How far does the rock travel horizontally before striking the water? (Neglect air resistance)

Accepted Answer

$$14.3\ \mathrm{m}$$

Question 16

An object is moving with constant non-zero velocity. Which of the following statements about the object must be true?

Accepted Answer

The net force on the object is zero.

Question 17

A $$10.0\ \mathrm{kg}$$ picture is held in place by two wires, one hanging at $$50^\circ to $$the left of the vertical and the second one at $$50^\circ to $$the right of the vertical. What is the tension in the first wire?

Accepted Answer

$$\dfrac{10.0 	imes 9.8}{2\cos50^\circ}$$

Question 18

A block of mass $$m is on a $$horizontal frictionless surface. A horizontal force $$F is $$applied for $$t$$ seconds. What is the speed of the block after the force has been applied?

Accepted Answer

$$\dfrac{F}{m}t$$

Question 19

A velocity vector $$\vec{A}$$ has a magnitude of $$6.0\ \mathrm{m/s}$$ and points $$30^\circ$$ north of east. Vector $$\vec{B}$$ has a magnitude of $$4.0\ \mathrm{m/s}$$ and points $$30^\circ$$ north of west. What is the magnitude of the resultant vector $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\sqrt{(6.0\cos30^\circ + 4.0\cos150^\$$circ)^2$$ + (6.0\sin30^\circ + 4.0\sin150^\$$circ)^2$$}$$

Kinematics, Vectors, and Projectile Motion: Study Notes and Problem Set

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