Question

A car is skidding out of control on a horizontal icy
(frictionless) road. It has a mass of 2000 kg and it is headed directly at Lois Lane at a speed of 45.0 m/s. When the car is 200 m from her, Superman begins to exert a steady force on the car, F, relative to the horizontal with a mag-
nitude of 1.30 X 10^4N (he's a strong dude) at a down-
ward angle of 30°. Was Superman correct? Was this force enough to stop the car before hitting Lois?

Answer 1

The force of 1.30x10⁴ N (relative to the horizontal) applied by Superman on a car that has a mass of 2000 kg and that is skidding out of control on a horizontal icy road, at a speed of 45.0 m/s, is enough to stop the car before hitting Lois Lane which is 200 meters away.    

           

To know if the applied force is enough to stop the car before hitting Lois, we need to find the distance after the force is exerted on the car, with the following equation:

$v_{f}^{2} = v_{i}^{2} + 2ad$  (1)

Where:

$v_{f}$: is the final velocity = 0 (when the car stops)

$v_{i}$: is the initial velocity = 45.0 m/s

a: is the acceleration

d: is the distance =?

First, we need to find the acceleration. We can do it by adding the forces acting on the x-direction (with Newton's second law):

$\Sigma F_{x} = ma$

$-Fcos(\theta) = ma$   (2)

Where:

F: is the force exerted by Superman = 1.30x10⁴ N  

θ: is the downward angle = 30°

m: is the mass of the car = 2000 kg

Now, solving equation (2) for "a" we have:

$a = -\frac{Fcos(\theta)}{m} = -\frac{1.30 \cdot 10^{4} N*cos(30)}{2000 kg} = -5.63 m/s^{2}$

The minus sign is because the car starts to decelerate after Superman applies the force.    

Then, the distance is (eq 1):

$d = \frac{v_{f}^{2} - v_{i}^{2}}{2a} = \frac{0 - (45.0 m/s)^{2}}{-2*5.63 m/s^{2}} = 179.8 m$

We can see that the car stops 20 meters away from Lois, therefore the force applied by Superman is enough.    

You can find more about Newton's second law here: https://brainly.com/question/23845187?referrer=searchResults

           

I hope it helps you!