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- If vectors A and B are orthogonal, what is the component of B along the direction of A ? What Is the component of A along the direction of B ?A proton in a synchrotron is moving in a circle of radius 1 km and increasing its speed by v(t)=c1+c2t2 , where c1=2.0105m/s,c2=105m/s3 . (a) What is the proton’s total acceleration at t=5.0s ? (b) At what tine does the expression for the velocity become unphysical?The arc length formula says the length sof arc subtended by angle in a circle of radius r is given by the equation s=r . What are the dimensions of (a) s, (b) r , and (c) ?
- A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?Two speedboats are traveling at the same speed relative to the water in opposite directions in a moving river. An observer on the riverbank sees the boats moving at 4.0 m/s and 5.0 m/s. (a) What is the speed of the boats relative to the river? (b) How fast is the river moving relative to the shore?The CERN particle accelerator is circular with a circumference of 7.0 km. (a) What is the acceleration of the protons (m=1.671027kg)that move around the accelerator at 5of the speed of light? (The speed of light is v=3.00108m/s .) (b) What is the force on the protons?
- Check Your Understanding How much work is done by the first dog and by the second dog In Example 2.16 on the displacement in Example 2.17?Check Your Understanding A boat heads north in still water at 4.5m/s directly across a river that is running east at 3.0 m/ s. What is the velocity o the boat with respect to Earth?What do vectors and scalars have in common? How do they differ?
- Starting at the island of Moi in an unknown archipelago, a fishing boat makes a round trip with two stops at the islands of Noi and Poi. It sails from Moi for 4.76 nautical miles (nmi) in a direction 37 north of east to Noi. From Noi, it sails 69 west of north to Poi. On its return leg from Poi, it sails 28 east of south. What distance does the boat sail between Noi and Poi? What distance does it sail between Moi and Poi? Express your answer both in nautical miles and in kilometei. Note: 1 nmi = 1852m.A truck is traveling east at 80 km/h. At an intersection 32 km ahead, a car is traveling north at 50 km/h. (a) How long after this moment will the vehicles be closest to each other? (b) How far apart will they be at that point?(a) A car speedometer has a 5% uncertainty. What is the range of possible speeds when it reads 90 km/h? (b) Convert this range to miles per how. Note 1 km = 0.6214 mi.