Question

a 16.0 kg sled initially at rest, slides down a frictionless hill that is inclined at 23.8^{\circ}.

if the hill is 18.5 m long, how long does it take for the sled to reach the bottom?

a = 3.95 m/s^2

t = ? s

Explanation:

⚡ Using what you learned: newton's laws of motion

Step 1: Identify given values

$$
LATEXBLOCK0
$$

Step 2: Relate distance, acceleration, and time

$$ d = v_i t + \frac{1}{2} a t^2 $$

Since \( v_i = 0 \):

$$ d = \frac{1}{2} a t^2 $$

Step 3: Solve for time \( t \)

$$ t = \sqrt{\frac{2d}{a}} $$

$$ t = \sqrt{\frac{2 \times 18.5}{3.95}} $$

$$ t = \sqrt{\frac{37}{3.95}} \approx \sqrt{9.367} \approx 3.06\text{ s} $$

Answer:

3.06