Final answer:
The speed of the cart when a 10-N force is applied at a 45° angle below the horizontal and it has been pushed 8.0 m is closest to 2 m/s, which can be found by first determining the horizontal component of the force and then calculating the resulting acceleration and velocity.
Step-by-step explanation:
To determine the speed of the cart when a 10-N force is applied at an angle of 45° below the horizontal, we first need to calculate the horizontal component of the force. This can be found using trigonometric functions: the horizontal component (Fx) is F cos(θ), where F is the force and θ is the angle. Plugging in the values, Fx = 10 N × cos(45°) = 7.07 N.
Next, we apply Newton's second law (F = m × a) to find the acceleration. Since F = 7.07 N and the mass (m) is 20 kg, the acceleration (a) is given by a = Fx/m = 7.07 N / 20 kg = 0.3535 m/s².
With the acceleration known, we can use the kinematic equation v² = u² + 2ad, where v is the final velocity, u is the initial velocity (0 m/s since the cart is initially at rest), a is the acceleration, and d is the distance (8.0 m). Solving for v gives v = √(2 × 0.3535 m/s² × 8.0 m) = √(5.656) m²/s² = 2.378 m/s.
Our final answer is slightly higher than option b) 2 m/s, but none of the answer choices exactly match our calculation. Therefore, the closest answer to the calculated speed is 2 m/s, which would be option b).