3. Bo and Luke Duke are running from Roscoe P. Coltrane and are going to jump th

Question

3. Bo and Luke Duke are running from Roscoe P. Coltrane and are going to jump the General Lee (their car) over the Hazard River. The river is 23m across, and there is a 1.5m high pile of dirt at the edge of the river that makes an angle of 33 degrees above the horizontal. They will use this pile of dirt as a launch ramp to get over the river. a. What is the slowest that Luke can drive the car so that it will make the jump over the river? 14.97 m/s b. How high does the General Lee get at this speed? 4.89 m c. How much time do Bo and Luke spend in the air? 1.831 s

Explanation / Answer

Horizontal distance = 23 m

Let velocity by v

Horizontal velocity = v cos 33 = 0.8387 v

Vertical velocity = v sin 33 = 0.5446 v

Time of flight = 23 / 0.8387v = 27.42/v seconds

Vertical distance moved = -1.5 m

=> -1.5 = 0.5446 v * (27.42/v) - 0.5 * 9.81 * (27.42/v)2

=> v = 14.98 m/s

a) Slowest they can drive = 14.98 m/s

b) maximum height = 1.5 + (0.5446*14.98)2/(2*9.81) = 4.89 m

c) time spend in air = 23 / 14.98 cos33 = 1.83 second

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