A 1,400-kg car traveling east with a speed of 30.6 m/s collides at an intersecti

Question

A 1,400-kg car traveling east with a speed of 30.6 m/s collides at an intersection with a 2,400-kg truck travelling north at a speed of 23.3 m/s.

The eastbound car is driven by an off-duty police officer, who knows her speed was exactly 25.0 m/s. From studying the angle (and the mass of the two vehicles), she concluded that the truck was over the speed limit of 90 km/h driving on that secondary road. Of course, the truck also failed to stop before entering the main road. If the truck were not speeding, what should be the maximum angle for (in degrees) in this accident?

theta < or = ________ degrees

Explanation / Answer

information like mass of car and mass of truck is missing .

They are required to get the final answer.

So i will assume all variable, You can put values and get answer.

mass of car = m    speed of car = v i   (in m/s)

mass of truck = M    speed of truck = V j   (in m/s)

final speed of both together = vf , angle with east = @

Using momentum conservation,

initial momentum = final momentum

mvi + MVj = (m + M) vf(cos@i + sin@j)

mvi + MVj = (m + M)vf cos@ i + (m + M)sin@ j

along i vector,

(m + M)vf cos@ = mv ......(i)

along j vector,

(m + M)vf sin@ = MV .........(ii)

(ii) / (i)

tan@ = MV / mv

@ = tan^-1(MV / mv)

plug in values and get theta Or put theta get V.(speed of truck)

if truck was in speed limit then ,

V = 90 km / hr = 90 x 1000 m / 3600 s = 25 m/s

for maximum angle within limit

@_max = tan^-1( 25M / 25m) = tan^-1( M/m)

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