Polar coordinate system and rectangular coordinate

Reference no: EM13930255

Question 1: A wall is being painted inside a workplace. There are four walls of equal size and area. Each wall is 3.46m high and 17.12m long. Find the area of the four walls, retaining the proper number of significant figures.

Question 2: a) If a car is travelling at a speed of 97 feet per second, is it exceeding the speed limit of 100km/h?

b) If you were travelling at 35km/h, how far, in feet, would you travel in 4 minutes and 24 seconds?

Question 3: (a) The rectangular coordinates of a point in the x-y plane are (??,??)=(2.75, -6.10). Draw this point and label the axes and the point appropriately. Then find the polar coordinates of this point.

(b) Convert (??,??)=(8.44mm, 23°) to Cartesian coordinates. Draw this point using both the polar coordinate system and the rectangular coordinate system.

Question 4: Figure below shows a person walking in a field. Find (a) the average velocity from O to C; (b) the average and instantaneous velocities from O to A; (c) the approximate instantaneous velocity at t=6 seconds; and (d) the average and instantaneous velocity at t=9 seconds.

2308_Average and instantaneous velocity.jpg

Question 5: A typical jetliner lands at a speed of approximately 155mi/h and decelerates at a rate of approximately 9.5mi/h per second. If the plane travels at a constant speed of 155mi/h for 1.0s after landing before applying the brakes, what is the total distance travelled by the plane between touchdown and coming to a complete stop? Present your answer in metres. Draw a diagram to best
illustrate your process.

Question 6: A stone is thrown from the top of a building with an initial velocity of 20.0m/s straight upwards, at an initial height of 50.0m above the ground. The stone started falling down to earth. Determine: (a) the time needed for the stone to reach its maximum height; (b) the maximum height; (c) the time needed for the stone to return to the height from which it was thrown and the velocity of the stone at that point; (d) the time needed for the stone to reach the ground and the velocity of the stone as it hits the ground. Draw a diagram which shows all the relevant distances, times and velocities.

Question 7: Graphically determine the magnitude and direction of the displacement if a cyclist rides 60.0km 30 degrees north of west and then rides due south 15.0km. Draw the diagram, showing all the relevant lines and labels.

Question 8: A jet plane travelling horizontally at 100m/s drops a rocket from a height of 1km. The rocket immediately fires its engines, accelerating at 20.0m/s2 in the ??-direction while falling under the influence of gravity along in the ??-direction. As the rocket hits the ground, find (a) its velocity in the ??-direction; (b) its velocity in the ??-direction; (c) the magnitude and direction of its velocity. Draw a
diagram which shows all the relevant distances, times and velocities.

Question 9: A concrete load weighing 29,430N hangs from a vertical cable (cable 3) tied to two other cables that are supported by a crane (cable 1 and cable 2 respectively). The two cables make an angle with the horizontal crane support of 43 degrees and 17 degrees respectively (as shown in the diagram). Find the tension in each of the three cables.

426_horizontal crane support.jpg

Question 10: Vehicle 1 of mass 1,545kg travelling at 90km/h collides into the back of Vehicle 2 of mass 1,830kg travelling at 60km/h. What are their post-impact speeds and delta v? Draw a diagram, showing the vehicles before impact, at impact and after the impact, labelling appropriately.

Question 11: Vehicle 1 of mass 1,760kg travelling at unknown speed collides into the back of Vehicle 2 of mass 1,385kg travelling at 45km/h. After the collision, Vehicle 1 travels 15m with wheels locked and sliding on a surface with a coefficient of friction of 0.65. Similarly, Vehicle 2 also slides with wheels locked on the same surface, but it slides 18m. What is pre impact speed of Vehicle 1 and what delta v have the vehicles undergone. Draw a diagram, showing the vehicles before impact, at impact and after the impact, labelling appropriately.

Question 12: Calculate the initial kinetic energy of a 1,750kg vehicle that braked 35m along a road surface with a coefficient of friction of 0.73.

Question 13: Calculate the coefficient of static and dynamic friction of a 54.0kg object on the ground which requires only 31.4kg to maintain movement but in order to initiate movement, one has to push it with a force of 440N.

Question 14: Calculate time taken to stop from an initial travelling speed of 85km/h on dry and travelled asphalt surface with locked and sliding braking. Remember that there are two answers, so your answer is a range. Use the friction table below to assist you in finding the appropriate coefficients of friction.

807_appropriate coefficients of friction.jpg

Question 15: Calculate deceleration of a vehicle that braked to a stop from 100km/h in 45m. Present your answer in both SI units and ‘g' forces.

Question 16: You arrive at a collision scene of a vehicle collision with a pedestrian. You observe some skid marks on the road and you measure them to be 35m long. You make an educated assumption that the vehicle was travelling at above 48km/h. The road surface is wet and is travelled and polished asphalt. Calculate the range of initial travelling velocities of the vehicle (assuming the pedestrian had
no impact on the deceleration of the vehicle). Use the friction table from Question 14 to assist you. As it was a residential zone, the speed limit for the road is 50km/h. Was the driver exceeding the speed limit prior to braking?

Question 17: A light aircraft flying in foggy weather missed the runway and crashed into a grass field nearby. Upon arrival at the accident scene you realise that the plane is fitted with a single two blade propeller at the front of the plane. You also observe what appear to be blade marks; cuts in the grass that are consistent with a rotating propeller. There are a number of these before the impact point between the plane and the ground. You know that the propeller on this particular aircraft rotates at 2,000 full revolutions per minute. You take a tape measure out and measure the distance between corresponding cuts to be 625mm. Using this information, calculate the approximate travelling speed of the aircraft just before impact with the ground. Present your answer in km/h.

Reference no: EM13930255

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