Please help with both parts! A car moves along a horizontal road with constant v

Question

Please help with both parts!

A car moves along a horizontal road with constant velocity v_0 = v_0xi until it encounters a smooth inclined hill, which it climbs with constant velocity V_1 = v_1xi + v_1yj as indicated in the figure. The car uniformly and instantaneously changes its velocity at the road-hill intersection. Let the origin of the Cartesian coordinate system be at the car's initial position. If the car moves for equal times along the road and hill, create an expression for its average velocity vector v_ave in terms of v_0x, v_1x, and v_1y during the total time interval and the unit vectors i and j. v_ave = (x_1x - v_0x)i + v_1yj Create an expression for the direction of the car's acceleration in terms of v_0x, v_1x, and v_1y during the transition between the horizontal surface and the hill. Express the answer in terms of tan(theta), where theta is the angle of the acceleration vector relative to the horizontal.

Explanation / Answer

Here ,

v0 = vox i

v1 = v1x i + v1y j

part a)

for the average velocity

Vave = (v0 * t + v1 * t)/(2 * t)

Vave = (vox i * t + (v1x i + v1y j )* t)/(2 t)

Vave = ((vox + v1x ) i + v1y j )/2

part b)

for the direction of car's acceleration

a = ((v1x i + v1y j ) - vox i )/t

tan(theta) = (v1y)/(v1x - v0x)

the expression for the direction is (v1y)/(v1x - v0x)

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