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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 hockey puck glides across the ice at \(27.7 \mathrm{~m} / \mathrm{s}\), when a player whacks it with her hockey stick, giving it an acceleration at \(64.3^{\circ}\) to its original direction. The acceleration lasts \(50.3 \mathrm{~ms}\), and the puck's displacement during this time is \(1.76 \mathrm{~m}\). Find the magnitude of the puck's acceleration.
A ferryboat sails between towns directly opposite each other on a river, moving at speed \(v^{\prime}\) relative to the water. (a) Find an expression for the angle it should head at if the river flows at speed \(V\). (b) What's the significance of your answer if \(V>v^{\prime}\) ?
How fast would a car have to round a 50 -m-radius turn for its acceleration to be numerically equal to that of gravity?
You walk \(1.57 \mathrm{~km}\) north, then \(0.846 \mathrm{~km}\) east. Find (a) the magnitude of your displacement vector and (b) its direction, expressed as an angle relative to the northward direction.
Your medieval history class is constructing a trebuchet, a catapult-like weapon for hurling stones at enemy castles. The plan is to launch stones off a 75-m-high cliff, with initial speed \(36 \mathrm{~m} / \mathrm{s}\). Some members of the class think a \(45^{\circ}\) launch angle will give the maximum range, but others claim the cliff height makes a difference. What do you give for the angle that will maximize the range?
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