Question

starting from rest, a car accelerates at 2 m/s^2 up a hill that is inclined 5.5 dagrees above the horizontal. How far a) horizontally and b) vertically has the car traveled in 12 s.

Answer 1

Question 15372

The initial velocity is $v_{0} = 0$ ( $v_{0\mathrm{s}} = 0, v_{0\mathrm{p}} = 0$ ). The acceleration is

$a_{x} = a\cos \varphi, a_{y} = a\sin \varphi, a = 2, \varphi = 5.5$ degrees. Hence, the horizontal and vertical displacements are $S_{x} = \frac{a_{x}t^{2}}{2} = \frac{a\cos\varphi t^{2}}{2}, S_{y} = \frac{a_{y}t^{2}}{2} = \frac{a\sin\varphi t^{2}}{2}$ , and are equal to $S_{x} \approx 143.34\mathrm{m}, S_{y} \approx 13.8\mathrm{m}$ .