Final answer:
The total time the car is in the air is 1.22 seconds and its horizontal speed is 2.13 m/s.
Step-by-step explanation:
To find the total time the car is in the air, we can solve for the time it takes for the car to fall from the table to the ground. We can use the equation:
h = (1/2) * g * t^2
where h is the height of the table (6 meters), g is the acceleration due to gravity (9.8 m/s^2), and t is the time in seconds. Rearranging the equation to solve for t, we get:
t = sqrt(2 * h / g) = sqrt(2 * 6 / 9.8) = 1.22 seconds.
The total time the car is in the air is the time it takes for the car to fall from the table plus the time it takes for the car to travel horizontally. Since the car lands 2.6 meters from the base of the table, we can calculate the time it took for the car to travel horizontally using the equation:
d = v * t
where d is the distance (2.6 meters), v is the horizontal velocity, and t is the time. Rearranging the equation to solve for t, we get:
t = d / v = 2.6 / v.
Equate two expressions we have:
1.22 = 2.6/v => v = 2.6/1.22 => v = 2.13 m/s.
So, the total time the car is in the air is 1.22 seconds and its horizontal speed is 2.13 m/s.