A model is created to investigate the impact force that cars create when release

Question

A model is created to investigate the impact force that cars create when released from various distances. A ramp is constructed at a 25° angle. A force sensor is placed at the end of the ramp to measure the impact of a model car. The car’s distance from the sensor is recorded before the car is released. Data collected for two bumpers is provided in the tables. Below is a picture of the simulation.



Distance from the sensor Impact from first bumper
7 cm 0.979
11 cm 1.231
18 cm 1.542
23 cm 1.679
29 cm 2.001

Distance from the sensor Impact from second bumper
7 cm 0.555
11 cm 0.703
18 cm 0.869
23 cm 0.997
29 cm 1.171

Use your own paper to plot the points and to determine, for each bumper, the algebraic function for the force, f, for any value of distance, d. (Hint: find the a-value of ). Describe the method you used to find a. Give the value of a correct to the nearest hundredth.


For each bumper, determine the distance the car must be from the force sensor so that it produces a force less than 0.75 newtons. Show algebraically how to find that force. Give answers correct to nearest hundredth.


Find the distance (to the nearest hundredth) where force produced by bumper one is one newton greater than the force produced by bumper two. Explain your reasoning.

Explanation / Answer

f=avd; Solve for a; Square both sides to solve for a - a = f/vd plug in values for f and d: First bumper a = 0.37,0.37,0.36,0.35,0.37 Second Bumper a = 0.21,0.21,0.21,0.21,0.22 2) First Bumper - 0.75 < .37*vd; 0.75/.37

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