Question

question 24
a child pulls a sled along frictionless snow with a rope at an angle θ = 38°. the child pulls with a force of f = 25 n and the rider and sled have a combined mass of 45 kg.
what is the resulting acceleration of the rider and sled?
image of a child pulling a sled with a rope at an angle θ
○ 0.55 m/s²
○ 0.44 m/s²
○ 1.2 m/s²
○ 2.3 m/s²

Explanation:

Step1: Find horizontal force component

The horizontal component of the force \( F \) is \( F_{x}=F\cos\theta \). Given \( F = 25\,\text{N} \) and \( \theta=38^\circ \), we calculate \( F_{x}=25\cos(38^\circ) \). Using \( \cos(38^\circ)\approx0.7880 \), we get \( F_{x}\approx25\times0.7880 = 19.7\,\text{N} \).

Step2: Apply Newton's second law

Newton's second law is \( F = ma \), so \( a=\frac{F_{x}}{m} \). The mass \( m = 45\,\text{kg} \), so \( a=\frac{19.7}{45}\approx0.44\,\text{m/s}^2 \).

Answer:

\( 0.44\,\text{m/s}^2 \) (corresponding to the option "0.44 m/s²")