Q: A projectile is launched horizontally from a $$45\,\mathrm{m}$$ high cliff. How long does it take to reach the ground?

$$\sqrt{\frac{2 \times 45}{9.8}}$$

Question 1

A kayaker needs to paddle north across 100 m of a swift river. The river flows east at $$2.0\,\mathrm{m/s}. If $$the kayaker can paddle at a speed of $$3.0\,\mathrm{m/s}$$ relative to the water, what is the kayaker's velocity relative to the ground?

Accepted Answer

$$\sqrt{2.0^2$ + 3.0^2$}\,\mathrm{m/s}$$ north-east

Question 2

A single-play vinyl record rotates on a turntable at $$45\,\mathrm{rpm}. $$What is the angular velocity in $$\mathrm{rad/s}$$?

Accepted Answer

$$4.71\,\mathrm{rad/s}$$

Question 3

A runner completes one lap around a $$400\,\mathrm{m}$$ track in $$50\,\mathrm{s}. $$What is the runner's average velocity?

Accepted Answer

$$0\,\mathrm{m/s}$$

Question 4

A ball is thrown straight up with an initial speed $$v_0. $$When it returns to the ground, what is its speed (neglecting air resistance)?

Accepted Answer

$$v_0$$

Question 5

A projectile is launched at an angle $$	heta$$ above the horizontal with speed $$v_0. $$What is the time of flight?

Accepted Answer

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

Question 6

A car travels $$60\,\mathrm{km}$$ east, then $$80\,\mathrm{km}$$ north. What is the magnitude of the displacement?

Accepted Answer

$$100\,\mathrm{km}$$

Question 7

A ball rolls off a table $$1.2\,\mathrm{m}$$ high with a horizontal speed of $$2.0\,\mathrm{m/s}. $$How far from the base of the table does the ball land?

Accepted Answer

$$0.98\,\mathrm{m}$$

Question 8

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 9

A rock is thrown horizontally from a $$20\,\mathrm{m}$$ high cliff with a speed of $$5.0\,\mathrm{m/s}. $$How long does it take to hit the ground?

Accepted Answer

$$2.02\,\mathrm{s}$$

Question 10

A ball is thrown at $$20\degree$$ above the horizontal with a speed of $$15\,\mathrm{m/s}. $$What is the maximum height reached?

Accepted Answer

$$\frac{(15 \sin 20\$$degree)^2$$}{2g}$$

Question 11

A train moves at $$30\,\mathrm{m/s}$$ east. A passenger walks at $$5\,\mathrm{m/s}$$ relative to the train, toward the back. What is the passenger's velocity relative to the ground?

Accepted Answer

$$25\,\mathrm{m/s}$$\ east

Question 12

A projectile is launched horizontally from a $$45\,\mathrm{m}$$ high cliff. How long does it take to reach the ground?

Accepted Answer

$$\sqrt{\frac{2 	imes 45}{9.8}}$$

Question 13

A ball is thrown at $$10\,\mathrm{m/s} at an $$angle of $$30\degree$$ above the horizontal. What is the horizontal component of its velocity?

Accepted Answer

$$10 \cos 30\degree$$

Question 14

A car accelerates from rest at $$2.0\,\mathrm{m/s^2$}$$ for $$5.0\,\mathrm{s}. $$What is its final velocity?

Accepted Answer

$$10\,\mathrm{m/s}$$

Question 15

A ball is dropped from rest from a height $$h. $$What is its speed just before hitting the ground?

Accepted Answer

$$\sqrt{2gh}$$

Physics with Calculus: Kinematics, Vectors, and Projectile Motion – Study Notes & Problem Solutions

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