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Chapter 3: Q.7CQ (page 119)
Explain why it is not possible to add a scalar to a vector.
The reading obtained from any sum of a vector and a scalar is always wrong and it is impossible to add them.
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An arrow is shot from a height of \(1.5{\rm{ m}}\) toward a cliff of height \(H\). It is shot with a velocity of \(30{\rm{ m}}/{\rm{s}}\) at an angle of \(60^\circ \) above the horizontal. It lands on the top edge of the cliff \(4.0{\rm{ s}}\) later.
(a) What is the height of the cliff?
(b) What is the maximum height reached by the arrow along its trajectory?
(c) What is the arrow's impact speed just before hitting the cliff?
Find the following for path B in Figure:
(a) the total distance traveled, and
(b) the magnitude and direction of the displacement from start to finish.
The various lines represent paths taken by different people walking in a city. All blocks are m on a side.
Suppose you first walk 12.0 m in a direction 20潞 west of north and then 20.0 m in a direction 40.0潞 south of west. How far are you from your starting point and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in Figure 3.56, then this problem finds their sum R = A + B.)
Verify the ranges for the projectiles in Figure 3.41 (a) for and the given initial velocities.
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