1) A Ford Mustang can accelerate from 0 to 60 mph in a time of 5.2 s. A Mini Coo

Question

1) A Ford Mustang can accelerate from 0 to 60 mph in a time of 5.2 s. A Mini Cooper isn't capable of such a rapid start, but it can turn in a very small circle 36 ft in diameter. How fast would you need to drive the Mini Cooper in this tight circle to match the magnitude of the Mustang's acceleration?

2) Mary needs to row her boat across a 100 m-wide river that is flowing to the east at a speed of 1.5 m/s. Mary can row the boat with a speed of 2.0 m/s relative to the water. If Mary rows straight north, how far downstream will she land?

3) A boat takes 4.0 hr to travel 36 km down a river, then 6.0 hr to return. How fast is the river flowing?

Explanation / Answer

1) The speed of Ford is v = 60 mph = 26.8224 m/s The time taken to accelerate t = 5.2 s The acceleration of ford is a = (v-u)/t a = (26.8224 m/s - 0)/5.2 s a = 5.158 m/s2 The radius of the circular path is R = 18 ft = 5.4864 m The acceleration in the circular path is a = v2/R v = (5.158 m/s2)(5.4864 m) v = 5.319 m/s 2) The speed of the boat relative to water is vbw = 2 m/s The width of the river is D = 100 m The speed of the river is vr = 1.5 m/s As the time taken by the boat to travell both horizontal and vertical distances is same, vbw/vr = vbw t/vr t vbw/vr = D/x x is the lamd point of boat downstream 2/1.5 = 100/x x = 75 m 3) When the boat goes downstream, v + vr = 36 km/4hr v is the speed of the boat vr is the speed of river v + vr = 9 kmph When the boat goes upstream, v - vr = 36 km/6 hr v - vr = 6 kmph Therefore 2vr = 3 kmph vr = 1.5 kmph 2) The speed of the boat relative to water is vbw = 2 m/s The width of the river is D = 100 m The speed of the river is vr = 1.5 m/s As the time taken by the boat to travell both horizontal and vertical distances is same, vbw/vr = vbw t/vr t vbw/vr = D/x x is the lamd point of boat downstream 2/1.5 = 100/x x = 75 m 3) When the boat goes downstream, v + vr = 36 km/4hr v is the speed of the boat vr is the speed of river v + vr = 9 kmph When the boat goes upstream, v - vr = 36 km/6 hr v - vr = 6 kmph Therefore 2vr = 3 kmph vr = 1.5 kmph

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