A civil engineer wishes to redesign the curved roadway in the example What is the Maximum Speed of the Car? in such a way that a

car will not have to rely on friction to round the curve without skidding. In other words, a car of mass m moving at the designated speed can negotiate the curve even when the road is covered with ice. Such a road is usually banked, which means that the roadway is tilted toward the inside of the curve. Suppose the designated speed for the road is to be v = 12.8 m/s (28.6 mi/h) and the radius of the curve is r = 37.0 m. At what angle should the curve be banked?

Physics

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A dog of mass 10 kg sits on a skateboard of mass 2 kg that is initially traveling south at 2 m/s. The dog jumps off with a veloc

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Answer:

17 m/s south

Explanation:

$m_1$ Mass of the dog = 10 kg

$m_2$ Mass of skateboard = 2 kg

v = Combined velocity = 2 m/s

$u_1$ Velocity of the dog = 1 m/s

$u_2$ Velocity of skateboard

In this scenario, linear momentum is conserved

$(m_1+m_2)v+m_1u_1+m_2u_2=0\\\Rightarrow u_2=-\dfrac{(m_1+m_2)v+m_1u_1}{m_2}\\\Rightarrow u_2=-\dfrac{(10+2)2+10\times 1}{2}\\\Rightarrow u_2=-17\ m/s$

The speed of the skateboard post-dog jump will be 17 m/s south, considering north as the positive direction

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