To find the speed of the sled after being towed up a ski hill, we first resolve the force applied by the rope into its horizontal and vertical components. Then, we use Newton's second law to find the horizontal acceleration of the sled. Finally, we use the kinematic equation to find the final speed of the sled.
To find the speed of the sled after being towed 14.0 m along the diagonal of the hill, we can use the principles of trigonometry and Newton's laws of motion.
First, we need to resolve the force applied by the rope into its horizontal and vertical components. The horizontal component of the force (Fhorizontal) can be found using the equation Fhorizontal = Ftension * cos(theta), where Ftension is the tension in the rope (274 N) and theta is the angle of the hill (17.5°). Fhorizontal = 274 N * cos(17.5°) = 257.8 N.
Next, we can use the equation Fhorizontal = m * a to find the horizontal acceleration (a) of the sled. Rearranging the equation, a = Fhorizontal / m. Since the sled is moving up the hill, the acceleration is negative. Substitute the values: a = -257.8 N / 48.7 kg = -5.29 m/s2.
Finally, we can use the kinematic equation v2 = u2 + 2as to find the final speed (v) of the sled. Rearranging the equation, v = sqrt(u2 + 2as), where u is the initial speed (0 m/s) and s is the distance traveled (14.0 m along the diagonal of the hill).
Substitute the values: v = sqrt(02 + 2 * (-5.29 m/s2) * 14.0 m) = 7.69 m/s.