2 0 202 Figure 721 Problem 7.50. 2 (c7p50) A 800- kg car collides with a 1400- k

Question

2 0 202 Figure 721 Problem 7.50. 2 (c7p50) A 800- kg car collides with a 1400- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 15.0 km/h in a direction of 20 with respect to the positive x axis. The heavier car moves at 18 km/h at -43 ° with respect to the positive x axis. What was the initial speed of the lighter car (in km/h)? Submit Answer Tries 0/12 What was the initial direction (as measured counterclockwise from the x-axis)? Submit Answer Tries 0/12

Explanation / Answer

Find the combined momenta of the cars:

p = (800kg*15km/h*cos20º + 1400kg*18km/h*cos-43º) i

+ (800kg*15km/h*sin20º + 1400kg*18km/h*sin-43º) j

p = 29706.4 kg·km/h i – 13082.1 kg·km/h j

This is the momentum after the collision but due to momentum conservation same is the momentum before the collision

Prior to the collision, all of that momentum was in the lighter car (since the heavier car was at rest).

Simply divide the total momentum by that car's mass to find its velocity:

v = p / 800kg = 37.133 km/h i – 16.35km/h j

If you need the magnitude, the

v = sqrt (37.133^2 + 16.35^2) = 40.57 km/h

= arctan(-16.35/37.133) = -23.76º (that is, below the x-axis)

Measured counterclockwise, that's = 360 + (23.76) = 336.24º.

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