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Chapter 3: Problem 22
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?
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(a) What's the magnitude of \(\hat{\imath}+\hat{\jmath} ?\) (b) What angle does it make with the \(x\)-axis?
A projectile launched at angle \(\theta\) to the horizontal reaches maximum height \(h\). Show that its horizontal range is \(4 h / \tan \theta\).
A basketball player is horizontally \(4.5 \mathrm{~m}\) from the center of the basket, which is \(3.05 \mathrm{~m}\) off the ground. At what angle should the player aim the ball from a height of \(2.5 \mathrm{~m}\) with a speed of \(8 \mathrm{~m} / \mathrm{s}\) ?
A carpenter tosses a shingle horizontally off an \(8.2-\mathrm{m}\)-high roof at \(14 \mathrm{~m} / \mathrm{s}\). (a) How long does it take the shingle to reach the ground? (b) How far does it move horizontally?
You throw a baseball at a \(45^{\circ}\) angle to the horizontal, aiming straight at a friend who's sitting in a tree a distance \(h\) above level ground. At the instant you throw your ball, your friend drops another ball. (a) Show that the two balls will collide, no matter what your ball's initial speed, provided it's greater than some minimum value. (b) Find an expression for that minimum speed.
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