A 2.1 x 10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20 with the horizontal. An average friction force of 4.0 x 10^3 N impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?

The length of the driveway is 4.98 m

Explanation:

Given that m = mass of car = 2.1 × 10³ kg, d = length of driveway,  f = frictional force = 4.0 × 10³ N, v = velocity of car at bottom of driveway = 3.8 m/s, u = speed of car at top of driveway = 0 m/s (since it starts at rest) and θ = slope of driveway = 20°

The component of the weight of the car along the driveway  minus the frictional force = the net force. So,

mgsinθ - f = ma where a = acceleration of the car

a = gsinθ - f/m

substituting the variables, we have

a = 9.8 m/s²sin20° - 4.0 × 10³ N/2.1 × 10³ kg

a = 3.352 m/s² - 1.905 m/s²

a = 1.447 m/s²

a ≅ 1.45 m/s²

Using v² = u² + 2ad, we find the length of the driveway, d. So,

d = (v² - u²)/2a

Substituting the values of the variables, we have

d = (v² - u²)/2a

d = ((3.8 m/s)² - (0 m/s)²)/(2 × 1.45 m/s²)

d = 14.44 m²/s² ÷ 2.9 m/s²

d = 4.98 m

So, the length of the driveway is 4.98 m

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west