Automobile collision-speed passenger crashes against dashboard

[physicsquest]

Homework Statement

In a collision, an automobile initially traveling at 50 km/h decelerates at a constant rate of 200 m/s^2. A passenger not wearing a seat belt crashes against the dashboard. Before the collision, the distance between the passenger and the dashboard was 0.60 m. With what speed, relative to the automobile, does the passenger crash into the dashboard? Assume that the passenger has no deceleration before contact with the dashboard.

initial velocity: 50 km/h= 13.89 m/s
a= -200 m/s^2
x-x0= 0.60 m

Homework Equations

x-x0= 1/2(v0+v)t
a= (v^2-vo^2)/2(x-x0)

The Attempt at a Solution

-200 m/s^2= (v^2-179.29 m^2/s^2)/1.2 m

answer is supposed to be 15.5 m/s.

 

[Dick]

The question asks for the velocity relative to the automobile. The initial velocity of the passenger relative to the automobile is 0m/sec. Try working it that way.

 

[tomcue]

I would approach this problem by using the equations of motion and the given information to calculate the final velocity of the passenger before impact with the dashboard.

Using the equation x-x0= 1/2(v0+v)t, we can rearrange it to v= (x-x0)/t + v0. Plugging in the values, we get v= (0.60 m)/(1 s) + 13.89 m/s = 14.49 m/s.

Next, using the equation a= (v^2-vo^2)/2(x-x0), we can solve for the final velocity (v) by rearranging it to v= sqrt(2a(x-x0)+vo^2). Plugging in the values, we get v= sqrt(2(-200 m/s^2)(0.60 m)+179.29 m^2/s^2) = 15.5 m/s.

Therefore, the passenger crashes into the dashboard with a final velocity of 15.5 m/s relative to the automobile.