1) One of the fundamental laws of motion states that the acceleration of an object is directly proportional to its mass

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1) One of the fundamental laws of motion states that the acceleration of an object is directly proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (b) The newton is the SI unit of force. According to the results for (a) how can you express a force having units of newtons by using the fundamental units of mass, length, and time?

2) Find the height or length of these natural wonders in kilometers, meters, and centimeters: (a) The longest cave system in the world is the Mammoth Cave system in Central Kentucky, with a mapped length of 348 miles. (b) In the United States, the waterfall with the greatest single drop is Ribbon Falls in California, which drops 1,612ft. (c) At 20, 320 feet, Mount McKinley in Alaska is America's highest mountain. (d) The deepest canyon in the United States is King's Canyon in California, with a depth of 8,200 ft.

3) One cubic centimeter (1.0 cm^3) of water has a mass of 1.0 X 10^-3 kg. (a) Determine the mass of 1.0 m^3 of water. (b) Assuming that biological substances are 98% water, estimate the mases of a cell with a diameter of 1.0 macrometer, a human kidney, and a fly. Take a kidney to be roughly a sphere with a radius of 4.0 cm and a fly to be roughly a cylinder 4.0 mm long and 2.0 mm in diameter.

4) A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.0,1.0), where the units are meters, what it the distance of the fly from the corner of the room?

5) A fountain of water if located at the center of a circular pool. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15.0 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to 55.0 degrees. How high is the fountain?

6) The radius of the planet Saturn is 5.85 X 10^7 m, and its mass is 5.68 X 10^26 kg. (a) Find the density of Saturn (its mass divided by its volume) in grams per cubic centimeter. (The volume of a sphere is given by (4/3) pi X r^3.) (b) Find the area of Saturn in square feet. (The surface area of a sphere is given by 4pi X r^2.)

7) Two boats start together and race across a 60-kn-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?

8) A tennis player moves in a straight-line path. Find her average velocity in the time intervals from (a) 0 to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 5.0 s, and (d) 0 to 5.0 s. Find the instantaneous velocities of the tennis player at (a) 0.50 s, (b) 2.0 s, (C) 3.0 s, and (d) 4.5 s.

9) Find the average age acceleration for an object during the time intervals 0 to 5.0 s, 5.0 s to 15 s, and 0 to 20 s. (b) Find the instantaneous acceleration at 2.0 s, 10 s, and 18 s.

10) A speedboat increases its speed uniformly from 20 m/s to 30 m/s in a distance of 200 m. Find (a) the magnitude of acceleration and (b) the time it takes the boast to travel 200-m distance.

11) A car starts from rest and travels for 5.0 s with a uniform acceleration of +1.5 m/s^2. The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s^2. If the brakes are applied for 3.0 s, (a) how fast is the car going at the end of the braking period, and (b) how far has the car gone?

12) A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to it the ground after it reaches its highest point? (d) What is the velocity when it returns to the level from which it started?

13) A parachutist with a camera descends in free fall at a speed of 10m/s. The parachutist releases the camera at an altitude of 50m. (a) How long does it take the camera to reach the ground? (b) What is the velocity of the camera just before it hits the ground?

14) Two students are on a balcony 19.6 m above the street. One student throws a ball vertically upward at the same speed. The second ball just misses the balcony on the way down. (a) What is the difference in the two balls' time in air? (b) What is the velocity of each ball as it strikes the ground? (c) How far apart are the balls 0.800 s after they are thrown?