A $1500-$kg mid$-$size car traveling east at $20\mathrm{.}0$ m$/$s $(44\mathrm{.}7$ mph$)$ collides with a $2000-$kg mid$-$size truck traveling north at $25$ m$/$s $(55\mathrm{.}9$ mph$).$ Assume that the cars lock together in such a way as to prevent them from separating or rotating significantly.

Part a

$(1$ points$)$

Calculate the distance that the locked cars will skid together assuming that the wheels stop turning after impact and a coefficient of kinetic friction of $0\mathrm{.}80$ between the rubber tires and the asphalt.

Please enter a numerical answer below. Accepted formats are numbers or $"$e$"$ based scientific notation e$.$g$.0\mathrm{.}23,-2,1$e$6,5\mathrm{.}23$e$-8$

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meters

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Part b

$(1$ points$)$

Calculate the magnitude of the velocity of the locked cars immediately after the impact.

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m$/$s

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Part c

$(1$ points$)$

Calculate the direction of the velocity of the locked cars after the collision. Give your answer as an angle relative to the east$-$pointing x$-$axis.

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degrees

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Part d

$(1$ points$)$

Calculate the kinetic energy lost $($absorbed by the two automobiles$)$ in the initial impact

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Joules

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Part e

$(1$ points$)$

For comparison, calculate the kinetic energy loss of the smaller car simply hitting an immovable brick wall head$-$on$.$

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Joules

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