The parachute on a race car that weighs

8036 N opens at the end of a quarter-mile
run when the car is traveling 39 m/s.
The acceleration of gravity is 9.81 m/s2 .
What net retarding force must be supplied
by the parachute to stop the car in a distance of 1270 m?
Answer in units of N.

Vf^2=Vi^2+2ad

0=39^2+2(NetForce/mass)*1270
solve for net force.

note that masscar= 8036/g

To find the net retarding force required to stop the car using the parachute, we can use the principles of Newton's second law which states that force is equal to mass multiplied by acceleration.

First, let's find the mass of the car. We know that weight (W) is equal to mass (m) multiplied by the acceleration due to gravity (g), which is 9.81 m/s^2.

Given: Weight (W) = 8036 N
Acceleration due to gravity (g) = 9.81 m/s^2

Using the formula: W = m * g, we can solve for m:
8036 N = m * 9.81 m/s^2

Divide both sides by 9.81 m/s^2:
8036 N / 9.81 m/s^2 = m
819.4 kg = m

Now that we have the mass of the car, we can proceed to calculate the net retarding force.

The net retarding force can be calculated using Newton's second law:
Force (F) = mass (m) * acceleration (a)

Given: Final velocity (vf) = 0 m/s (as the car needs to stop)
Initial velocity (vi) = 39 m/s
Distance (d) = 1270 m

The acceleration can be calculated using the equation:
vf^2 = vi^2 + 2a * d

Rearranging the equation to solve for acceleration:
a = (vf^2 - vi^2) / (2 * d)

Substituting the given values:
a = (0^2 - 39^2) / (2 * 1270) = (-1521) / 2540 ≈ -0.598 m/s^2

Note: The negative sign indicates that the acceleration is in the opposite direction to the car's initial motion.

Finally, we can calculate the net retarding force using Newton's second law:
F = m * a

Substituting the values:
F = 819.4 kg * (-0.598 m/s^2) ≈ -489.7 N

The net retarding force required to stop the car using the parachute is approximately 489.7 N (in the opposite direction of the car's motion).