91Ó°ÊÓ

Under what conditions is the magnitude of the vector sum \(A+B\) equal to the sum of the magnitudes of the two vectors?

Can two vectors of cqual magnitude sum to zero? How about two vectors of unequal magnitude?

Can an object have a southward acceleration while moving northward? A westward acceleration while moving northward?

Is there any point on a projectile's trajectory where velocity an acceleration are perpendicular?

You're in a bus moving with constant velocity on a level road when you throw a ball straight up. When the ball returns, does it land ahead of you, behind you, or back at your hand? Explain.

An ion in a mass spectrometer follows a semicircular path of radius \(15.2 \mathrm{cm} .\) What are (a) the distance it travels and (b) the magnitude of its displacement?

Find the magnitude of the vector \(34 \hat{\imath}+13 \hat{\jmath} \mathrm{m}\) and determine its angle to the \(x\) -axis.

A car drives north at \(40 \mathrm{mi} / \mathrm{h}\) for 10 min, then turns east and goes \(5.0 \mathrm{mi}\) at \(60 \mathrm{mi} / \mathrm{h} .\) Finally, it goes southwest at \(30 \mathrm{milh}\) for 6.0 min. Determine the car's (a) displacement and (b) average velocity for this trip.

An object's velocity is \(\vec{v}=c t^{3} \hat{\imath}+d \hat{\jmath},\) where \(t\) is time and \(c\) and \(d\) are positive constants with appropriate units. What's the direction of the object's acceleration?

A car, initially going eastward, rounds a \(90^{\circ}\) curve and ends up heading southward. If the speedometer reading remains constant, what's the direction of the car's average acceleration vector?