Q: A student estimates the mass of a $$900\ \mathrm{m}$$ tall skyscraper with a base diameter of $$230\ \mathrm{m}$$, treating it as a cone. If the density is $$19\ \mathrm{kg/m^3$}$$, what is the estimated mass?

$$3.6 \times 10^8$\ \mathrm{kg}$$

Question 1

Given two vectors $$\vec{M}$$ and $$\vec{N}$$ with magnitudes $$3.2\ \mathrm{m}$$ and $$2.3\ \mathrm{m}$$, both making $$48^\circ$$ with the $$x-$$axis but in opposite $$y-$$directions, what is the magnitude and direction of $$\vec{M} 	imes \vec{N}$$?

Accepted Answer

Magnitude = $$0.769$$, Direction = $$-z$$

Question 2

Given vectors $$\vec{A}$$ and $$\vec{B}$$, which of the following diagrams correctly represents $$\vec{A} - \vec{B}$$?

Accepted Answer

The diagram where $$-\vec{B} is $$added to $$\vec{A}$$ tail-to-head, and $$\vec{A} - \vec{B} is $$the resultant from the tail of $$\vec{A} to $$the head of $$-\vec{B}.$$

Question 3

Following the rules of significant figures, simplify the expression $$21.8/16.9.$$

Accepted Answer

$$1.3$$

Question 4

A particle moves in the wind with velocity $$\vec{v}_1 = (17\hat{i} - 6\hat{j})$$ mph for $$45$$ min. The wind changes, and the new velocity is $$\vec{v}_2 = (5\hat{i} + 18\hat{j})$$ mph for $$1.5 h. $$What is the total displacement in component form (mi)?

Accepted Answer

$$(20.3\hat{i} + 22.5\hat{j}) mi$$

Question 5

A student estimates the mass of a $$900\ \mathrm{m}$$ tall skyscraper with a base diameter of $$230\ \mathrm{m}$$, treating it as a cone. If the density is $$19\ \mathrm{kg/m^3$}$$, what is the estimated mass?

Accepted Answer

$$3.6 	imes 10^8$\ \mathrm{kg}$$

Question 6

A dog runs $$8.2\ \mathrm{km} to a $$park and returns to its cage in $$25$$ minutes. If the return is along the $$-x$$ direction, what is the average velocity (in m/s) for the return trip?

Accepted Answer

$$-5.47\ \mathrm{m/s}$$

Question 7

A $$450\ \mathrm{g}$$, $$42.0\ \mathrm{cm}$$ long projectile is launched nearly vertically. Using the velocity-time graph, estimate the acceleration at $$t=10\ \mathrm{ms}$$, $$t=25\ \mathrm{ms}$$, and $$t=40\ \mathrm{ms} if $$the velocity increases linearly to $$8\ \mathrm{m/s} at$$ $$t=40\ \mathrm{ms}.$$

Accepted Answer

$$a_{10} = 200\ \mathrm{m/s^2$}$$, $$a_{25} = 200\ \mathrm{m/s^2$}$$, $$a_{40} = 0\ \mathrm{m/s^2$}$$

Question 8

A Montgolfier balloonist, moving up at $$10.0\ \mathrm{m/s}$$, drops a bag of stones from $$50.0\ \mathrm{m}$$ above the ground. What is the speed and position of the bag $$0.50\ \mathrm{s}$$ after release?

Accepted Answer

$$v = 5.1\ \mathrm{m/s}$$, $$h = 53.8\ \mathrm{m}$$ above ground

Question 9

A van starts from rest with acceleration $$3.2\ \mathrm{m/s^2$}. A $$competitor van moves at $$22.0\ \mathrm{m/s}$$ and overtakes the first van. What is the speed of the first van at the moment of overtaking?

Accepted Answer

$$40\ \mathrm{m/s}$$

Question 10

A school bus travels $$140\ \mathrm{m} in$$ $$5.0\ \mathrm{s}$$, then brakes to rest in $$4.0\ \mathrm{s}. $$What is the magnitude of its acceleration in $$\mathrm{m/s^2$}$$ and in terms of $$g$$?

Accepted Answer

i) $$7.0\ \mathrm{m/s^2$}$$, ii) $$0.7g$$

Question 11

A velocity-time graph for a bicycle shows its highest velocity at $$t=35\ \mathrm{s}. At $$what time does the bicycle achieve its highest velocity?

Accepted Answer

$$t = 35\ \mathrm{s}$$

Question 12

A position-time graph for a vehicle shows $$x=80\ \mathrm{m} at$$ $$t=15\ \mathrm{s}$$ and $$x=60\ \mathrm{m} at$$ $$t=20\ \mathrm{s}. $$What is the instantaneous velocity at $$t=15\ \mathrm{s}$$?

Accepted Answer

$$-4.0\ \mathrm{m/s}$$

Question 13

A seed is fired at $$55\ \mathrm{m/s} at$$ $$54.0^\circ$$ above the horizontal. What are the horizontal and vertical components of velocity and acceleration at the highest point?

Accepted Answer

$$v_x = 32.3\ \mathrm{m/s}$$; $$v_y = 0$$; $$a_x = 0$$; $$a_y = -9.8\ \mathrm{m/s^2$}$$

Question 14

A rock slides off a mountain at $$22^\circ$$ below the horizontal with $$6.0\ \mathrm{m/s}$$ from a height of $$13\ \mathrm{m}. $$What is the horizontal distance to where it lands?

Accepted Answer

$$7.9\ \mathrm{m}$$

Question 15

A football is kicked from a cliff at $$30\ \mathrm{m/s}$$ and $$35^\circ. $$What is the angle of the ball's velocity after it has traveled $$75\ \mathrm{m}$$ horizontally?

Accepted Answer

$$-27.3^\circ$$

Question 16

A drone's velocity is given by $$\vec{v}(t) = [12 + (0.0928 t^3$)]\hat{i} + [2.05 t - 1.035 t^2$]\hat{j} (in m/s). $$What is the magnitude and direction of its velocity and acceleration $$3$$ seconds after launch?

Accepted Answer

Velocity $$= 17.025\ \mathrm{m/s}$$, $$41.07^\circ$$; Acceleration $$= 6.235\ \mathrm{m/s^2$}$$, $$275.12^\circ$$

Question 17

A thief must throw a pouch of diamonds over a $$4.0\ \mathrm{m}$$ high wall to a partner $$5.0\ \mathrm{m}$$ away. What is the minimum angle above the horizontal for the throw?

Accepted Answer

$$42.3^\circ$$

Question 18

Two circus artists ride unicycles. The red artist moves at $$1.5\ \mathrm{m/s}$$, the blue at $$-2.5\ \mathrm{m/s}. $$What is the speed of blue relative to red?

Accepted Answer

$$4.0\ \mathrm{m/s}$$

Physics Fundamentals: Vectors, Kinematics, and Applications – Study Notes

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