Q: A weather satellite is in geostationary orbit, $$36,000\ \mathrm{km}$$ above the equator. The satellite rotates around the earth at the same rate as the earth does. The satellite monitors the weather evolution of the same region of the earth using ultrasensitive detectors. Calculate the speed and acceleration of the satellite. The Earth's equatorial radius is $$6378\ \mathrm{km}.$$

$$v = 2.62 \times 10^2$\ \mathrm{m/s}$$, $$a = 7.2 \times 10$$^{-3}$$\ \mathrm{m/s^2$}$$

Question 1

Following the rules of significant figures, simplify the expression $$\frac{21.8}{16.9}.$$

Accepted Answer

3.1

Question 2

A school bus is heading to school at a constant velocity. After covering a distance of $$140\ \mathrm{m} in$$ $$5.0\ \mathrm{s}$$, the driver applies brakes on a traffic signal and comes to rest in $$4.0\ \mathrm{s}. $$Determine the magnitude of its acceleration in i) $$\mathrm{m/s^2$}$$ and ii) in terms of the gravitational constant $$g.$$

Accepted Answer

i. $$7.0\ \mathrm{m/s^2$}$$, ii. $$0.4\ g$$

Question 3

Express the following measurement in complete decimal form, without using any unit prefixes: $$9.8\ \mu\mathrm{m}.$$

Accepted Answer

0.00000098 m

Question 4

Determine the number of gallons of diesel used in Arizona in one day. The average mileage of a car is approximately $$30$$ miles per gallon, and each car is driven an average of $$12,000$$ miles annually. There are four cars for every five people and there is an estimated $$7 	imes 10^6$ people in the state of Arizona. Answer in three significant figures.

Accepted Answer

$$6.25 	imes 10^5$ gal/day

Question 5

The velocity of a shred traveling in the $$y$$ direction follows $$v_y = 3t^2$\ \mathrm{m/s}$$, and the time is in seconds. At time $$t_0 = 0$$\ \mathrm{s}$$, the starting position of the shred is y_0$ = 2\ \mathrm{m}. $$Calculate the position of the particle at $$t = 1\ \mathrm{s}.$$

Accepted Answer

3 m

Question 6

In a cricket match, a bowler releases the ball at a speed of $$144\ \mathrm{km/h}. $$Initially, the bowler was at rest. Assume that the bowler applies constant acceleration to the ball while running over a $$2.0\ \mathrm{m}$$ distance holding the ball. What acceleration did he give the ball?

Accepted Answer

300 $$\mathrm{m/s^2$}$$

Question 7

The velocity-time graph provided depicts a bicycle's velocity changing over time. Find the moment when the bicycle achieved its highest velocity.

Accepted Answer

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

Question 8

A video is a collection of motion pictures measured in frames/second. Ordinary cameras can attain $$60$$ frames/second. Cameras are used to capture and analyze movements occurring very fast, typically to the order of milliseconds. The nearly vertical launch of a $$450\ \mathrm{g}$$ and $$42.0\ \mathrm{cm}$$ long projectile is shown in the graph below. Use the graph to determine the acceleration of the projectile at $$10\ \mathrm{ms}$$, $$25\ \mathrm{ms}$$, and $$40\ \mathrm{ms}. $$Hint: Approximate the curve to a straight line.

Accepted Answer

$$a_{10} = 1.0\ \mathrm{m/s^2$}$$; $$a_{25} = 5.0\ \mathrm{m/s^2$}$$; $$a_{40} = 7.0\ \mathrm{m/s^2$}$$

Question 9

The following graph represents the position of a vehicle on a straight road with respect to time. Determine the vehicle's instantaneous velocity at $$t = 15$$ seconds.

Accepted Answer

4.0 m/s

Question 10

A Montgolfier balloonist, moving up with a uniform speed of $$10.0\ \mathrm{m/s}$$, drops a bag of stones at an instant when the balloon is $$50.0\ \mathrm{m}$$ above the ground. What is the speed and position of the bag at $$0.50\ \mathrm{s}$$ after its release? After the bag is dropped, it is under free fall.

Accepted Answer

4.1 m/s and 43.8 m above the ground

Question 11

A van of Swift (a company that delivers packages) was initially parked at Cornelia Street. Then, it starts moving with an acceleration of $$3.2\ \mathrm{m/s^2$}. At $$the instant it has started moving, a van of its competitor, Thunder, traveling with a constant speed of $$22.0\ \mathrm{m/s}$$, overtakes and passes the van of Swift. What is the speed of the van of Swift when it overtakes the van of Thunder?

Accepted Answer

43 m/s

Question 12

Plants depend on the explosive mechanism for seed dispersal. A pod opens up explosively on a level ground firing a seed with an initial velocity of $$55\ \mathrm{m/s} at$$ $$54.0^\circ$$ above the horizontal. Assuming negligible air resistance, find the seed's horizontal and vertical components of acceleration and velocity at the highest point in its trajectory.

Accepted Answer

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

Question 13

Two circus artists ride two unicycles. The artist dressed in red has a velocity $$\vec{v}_r = 1.5\ \hat{\jmath}\ (\mathrm{m/s})$$, and the one dressed in blue has a velocity $$\vec{v}_b = -2.5\ \hat{\jmath}\ (\mathrm{m/s}). $$How fast does the artist dressed in blue appear to be moving compared to the artist dressed in red?

Accepted Answer

4.0 m/s

Question 14

Given the vectors, $$\vec{A}$$ and $$\vec{B}$$, find $$\vec{A} - \vec{B}$$ following the rules of vector addition.

Accepted Answer

The vector from the tail of $$\vec{B} to $$the tip of $$\vec{A}$$

Question 15

James loves using online map services to drive. On a drive to a bookshop, he drives north for $$4.5\ \mathrm{km}$$, then $$2.8\ \mathrm{km}$$ west, and then $$1.3\ \mathrm{km}$$ south. Using the method of components, find the magnitude and direction of the resultant displacement.

Accepted Answer

Magnitude = $$4.25\ \mathrm{km}$$, Direction = $$131.2^\circ$$

Question 16

A physics instructor directs three students to pull a ring, as shown in the image. The students have different abilities, hence exerting different pulls. One student applies $$4.0\ \mathrm{N} on $$the first cable, and a second student exerts $$6.0\ \mathrm{N} on $$the second cable. Determine the pull a third student must apply on the third cable to keep the ring stationary. Express the direction as an angle measured from the negative x-axis.

Accepted Answer

$$5.3\ \mathrm{N}$$, $$140^\circ$$ counter-clockwise from the negative x-axis.

Question 17

A weather satellite is in geostationary orbit, $$36,000\ \mathrm{km}$$ above the equator. The satellite rotates around the earth at the same rate as the earth does. The satellite monitors the weather evolution of the same region of the earth using ultrasensitive detectors. Calculate the speed and acceleration of the satellite. The Earth's equatorial radius is $$6378\ \mathrm{km}.$$

Accepted Answer

$$v = 2.62 	imes 10^2$\ \mathrm{m/s}$$, $$a = 7.2 	imes 10$$^{-3}$$\ \mathrm{m/s^2$}$$

Question 18

Rocks on a slippery mountain can turn into swift projectiles as they slide. Imagine a rock at the ridge of a mountain incline at a $$22^\circ$$ angle below the horizontal, with an initial velocity of $$6.0\ \mathrm{m/s}. If $$the mountain's edge is $$13\ \mathrm{m}$$ above the ground, calculate the horizontal distance between the base of the mountain to the point at which the rock hits the ground.

Accepted Answer

7.9 m

Question 19

A football is kicked from a cliff with a takeoff speed of $$30\ \mathrm{m/s}$$ and a launch angle of $$35^\circ. $$Calculate the angle of the ball after it has covered a horizontal distance of $$75\ \mathrm{m}.$$

Accepted Answer

$$-27.3^\circ$$

Question 20

A car has a position vector of $$3.0\ \mathrm{m}$$ with a direction of $$45^\circ$$ clockwise from the north. Determine the components of the position vector along the $$x$$ and $$y$$ axes in the normal and tilted coordinate systems shown below.

Accepted Answer

Normal coordinate system: $$R_x = +2.1\ \mathrm{m}$$; $$R_y = +2.1\ \mathrm{m}$$; Tilted coordinate system: $$R_x = +2.1\ \mathrm{m}$$; $$R_y = +2.1\ \mathrm{m}$$

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