Suppose a car manufacturer tested its cars for front-end colli...

Question

Suppose a car manufacturer tested its cars for front-end collisions by hauling them up on a crane and dropping them from a certain height. What height corresponds to a collision at

(b) 35 km/h?

Accepted Answer

Hello everyone. Let's go through this practice problem. In a safety assessment for amusement park rides, engineers drop test dummies from different heights to model various collision scenarios. Calculate the height from which a test dummy should be dropped to simulate a collision at 25 kilometers per hour. Option. A 4.91 m B 6.94 m C 2.46 m and D 24.1 m. So this is a bit of a kinematics problem. But we're going to assume that the acceleration is constant and find the height that be required to give us a certain final speed first things first though we want to do a quick unit conversion because the final velocity is given to us as 25 kilometers per hour. But in order to do our math, especially since all our options are given in meters, we want to convert this into meters per second. So we're going to have to do a little chain link conversion here to convert from kilometers into meters and then from hours into seconds, the first off, we'll use the one that states that 1000 m is equivalent to one kilometer and we'll write it so that kilometers in the denominator so that it cancels out with the kilometers in the original speed. Then we'll convert from hours into seconds and recall that there are 3600 seconds for one hour. And this time I'm putting hours in the numerator so that it cancels out with the hours in the denominator and the original speed given to us. So we put all this into a calculator and we find a speed of 6.944 m per second. So that is our final speed in unit we can work with. Now, let's get to the actual kinematics uh problem recall that in problems like this, there are three different equations that we tend to work with. The final speed is equal to the initial speed plus acceleration multiplied by time displacement is equal to initial speed multiplied by time plus one half of the acceleration multiplied by the square of time. And final speed squared equals initial speed squared plus two multiplied by acceleration multiplied by displacement. Now recall any kinematics problems. The whole point is we want to choose the equation that includes the variable we're trying to find. But as everything else known, we're looking to calculate a height or displacement in this case, so we can ignore the first equation since it doesn't have that variable at all. And we're not told anything about time. So we can also ignore the second equation because we're not given that information and can't use it. So the third equation, the V squared equation is what we're gonna want to use. And we're gonna want to solve this equation for the displacement, which I wrote is delta X. But I guess in our case, it's actually gonna be more of a delta Y. So I'll do some algebra to solve for delta Y. And it's pretty simple algebra. We subtract V not squared from both sides of the equation and then divide both sides of the equation by two A. So delta Y is equal to V squared minus V not squared divided by two A. And that's really it. Now, we just gotta plug in the values that were given to us by the problem. So the final speed squared is we just established, the final speed is 6.944 m per second. Don't forget to square it minus the square of the initial speed. But the problem tells us that the dummy is being dropped. So the initial speed is just zero and zero squared is just zero. You can basically ignore that whole term and this is being divided by two multiplied by the acceleration. So two multiplied by the gravitational acceleration of 9.81 m per second squared. So I put this into a calculator and we find a height of about 2.46 m. And that is our answer to the problem which corresponds to option C so that is it for this problem. I hope this video helped you out and please consider checking out our other tutoring videos which will give you more experience with these types of problems. That's all for now. And I hope you have a lovely day. Bye bye.

Suppose a car manufacturer tested its cars for front-end collisions by hauling them up on a crane and dropping them from a certain height. What height corresponds to a collision at

(b) 35 km/h?

Key Concepts

Kinetic Energy

Gravitational Potential Energy

Conversion of Energy

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