Summarize the problem indicating the question to be answered, list the equations

Question

Summarize the problem indicating the question to be answered, list the equations used, show all math, and indicate your answer. A stunt man must drive a car off of the 3^rd floor of a parking garage and land on a hot dog stand on the street below. The car is initially parked, and the car will drive in a straight horizontal line with constant acceleration a distance of 14.0 m to the edge of the parking garage. After the car leaves the garage it becomes a projectile that must travel a horizontal distance of 12.0 m while it falls a vertical distance of 20.0 m. Assuming air resistance is negligible, what must be the acceleration of the car while it is driving on the parking garage?

Explanation / Answer

as vertical speed when the car drops from the parking garage is 0,if time taken to travel 20 m distance vertically is t seconds,

then using the formula:

initial speed*time+0.5*acceleration*time^2=distance covered

==>0*t+0.5*9.8*t^2=20

==>t=sqrt(20/4.9)=2.0203 seconds

during this time, horizontal distance travelled=12 m

then horizontal speed required=12/2.0203=5.9397 m/s

this speed is achieved with a constant acceleration, let say, a m/s^2 after travelling 14 m

initial speed for the 14 m travel =0 m/s

final speed=5.9397 m/s

then final speed^2-initial speed^2=2*acceleration*distance

==>5.9397^2-0^2=2*a*14

==>a=5.9397^2/28=1.26 m/s^2

hence acceleration of the car while driving on the parking garage is 1.26 m/s^2

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