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- One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 2.89km. They start at the west side of the lake and head due south to begin with. What is the distance they travel? What is the magnitude of the couple’s displacement? What is the direction (relative to due east) of the couple’s displacement?An engineer designs a roller coaster so that a car travels horizontally for 172 ft, then climbs 117 ft at an angle of 32.0° above the horizontal. It then moves 117 ft at an angle of 41.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.) magnitude= ? ft direction = ?° counterclockwise from the +x-axisA person in a rowboat is 3 km from a point P on a straight shore while his destination is 5m directly east of point P. If he is able to row 4 km per hour and walk 5 km per hour, how far from his destination must he land on the shore in order to reach his destination in the shortest possible?
- An engineer designs a roller coaster so that a car travels horizontally for 172 ft, then climbs 147 ft at an angle of 32.0° above the horizontal. It then moves 147 ft at an angle of 48.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.) Sig figs Considered.Most days after lunch, I like to take a stroll around campus ( given it’s not too hot ). Suppose on this day, I walk 4.38 meters 53.50 degrees north-east. If I then walk another 3.24 meters north, how far will I have to walk in a straight line to get back to the physics building where I started?An engineer designs a roller coaster so that a car travels horizontally for 182 ft, then climbs 117 ft at an angle of 32.0° above the horizontal. It then moves 117 ft at an angle of 48.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.) Magnitude = ? Direction = 356.5 degrees counterclockwise from the + x-axis
- In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running over the edge of the cliff above Ohio's Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. (Figure 1) A. Representing the horizontal distance jumped as L and the vertical drop as h , as shown in the figure, derive an expression for the minimum speed v he would need to make his leap if he ran straight off the cliff. Express your answer in terms of the given quantities and appropriate constants. B. Evaluate your expression for a 22 ft jump with a 20 ft drop to the other side. C. Is it reasonable that a person could make this leap? Use the fact that the world record for the 100 m dash is approximately 10 s to estimate the maximum speed such a runner would have. (Yes or no answer)Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity (in m/s) would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7 m/s2. (Assume the volcano is radially symmetric and the summit is at its center. Enter the magnitude.)In calm air a plane flying from the Pedimaxus International Airport can reach Cliffs of insanity in two hours by following a bearing of N8.2 degrees East at 96 miles an hour. (The distance between the airport and the cliffs is 192 miles. ) If the wind is blowing from the southwest at 25 miles per hour, what speed and bearing should the pilot take so that she makes the trip in two hours along the original heading?
- Starting at the origin, a person walks 350 meters in a direction 30.0° South of West, then 570 meters in a direction 35.0° West of North. If the person now wishes to walk in a straight line back to the origin, what must be the magnitude and direction of the displacement?Calculate the magnitude and direction of the resultant of the two vectors a) 50 km E and b) 70 km 60* NE.2) An airplane travels at 4.5 x 10^2 km due east and then travels an unknown distance due north. Finally, it returns to its starting point by travelling a distance of 525 km. How far did the airplane travelled due north?A commuter airplane starts from an airport and takes the route shown in Figure P3.19. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.