A 115 kg car is on a hill
that is inclined at .
What is the -component
of the weight of the car?

Ask by Hill Carroll. in the United States

Mar 22,2025

Question

A 115 kg car is on a hill that is inclined at $$ 37.0^{\circ} $$. What is the $$ y $$-component of the weight of the car? $$ w_{y}=[?] \mathrm{N} $$

UpStudy AI · Accepted Answer

Let's start by writing the weight of the car:

$$
w = mg
$$

where  
$$ m = 115 \, \mathrm{kg} $$ (mass of the car)  
$$ g = 9.8 \, \mathrm{m/s^2} $$ (acceleration due to gravity)

On an inclined plane, if we define the $$ y $$-axis as perpendicular to the incline, the $$ y $$-component of the weight is given by:

$$
w_y = mg \cos \theta
$$

with  
$$ \theta = 37.0^{\circ} $$ (angle of the incline)

1. Substitute the given values into the formula:

$$
w_y = (115 \, \mathrm{kg})(9.8 \, \mathrm{m/s^2}) \cos(37.0^{\circ})
$$

2. First, calculate the product $$ mg $$:

$$
mg = 115 \times 9.8 = 1127 \, \mathrm{N}
$$

3. Next, determine the cosine factor. Recall that:

$$
\cos(37.0^{\circ}) \approx 0.7986
$$

4. Finally, compute $$ w_y $$:

$$
w_y \approx 1127 \, \mathrm{N} \times 0.7986 \approx 900.6 \, \mathrm{N}
$$

Thus, the $$ y $$-component of the weight of the car is approximately:

$$
w_y \approx 901 \, \mathrm{N}
$$
The $$ y $$-component of the car's weight is approximately $$ 901 \, \mathrm{N} $$.

A 115 kg car is on a hill
that is inclined at .
What is the -component
of the weight of the car?