Final answer:
To find the speed of the cart when a constant 15 N force is applied at an angle of 45° below the horizontal, we can resolve the force into its horizontal and vertical components. Using the equations of motion, we can calculate the acceleration of the cart and then use the equation v^2 = u^2 + 2as to find the speed of the cart. The speed of the cart is 1.86 m/s.
Step-by-step explanation:
To find the speed of the cart when a constant 15 N force is applied at an angle of 45° below the horizontal, we can use the equations of motion and resolve the force into its horizontal and vertical components. The force has a vertical component equal to 15 N * sin(45°) and a horizontal component equal to 15 N * cos(45°). Since friction is negligible, the horizontal component of the force will provide the acceleration of the cart. Using the equation
a = F/m
where a is the acceleration, F is the force, and m is the mass of the cart, we can calculate the acceleration. Once we have the acceleration, we can use the equation
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity (which is 0 m/s since the cart is at rest), a is the acceleration, and s is the distance pushed, to find the speed of the cart.
Plugging in the values, we get:
a = (15 N * cos(45°)) / 30 kg = 0.25 m/s^2
v^2 = (0 m/s)^2 + 2 * 0.25 m/s^2 * 6.9 m = 0.25 m/s * 13.8 m = 3.45 m^2/s^2
v = sqrt(3.45) m/s = 1.86 m/s.