Final answer:
The force needed to push the go-cart up the hill depends on the angle of the slope, which isn't provided. The speed of the go-cart at the bottom can be found using conservation of energy, but precise calculations would require more data on the slope's specifications.
Step-by-step explanation:
The student's question involves calculating the force necessary to push a go-cart up a hill and the speed it will reach at the bottom of the hill. This question can be solved using concepts from physics such as gravitational force and energy conservation.
Part A: Force needed to push the go-cart up the hill
To determine the force required to push the go-cart up the hill, we need to calculate the component of gravitational force acting along the slope. The formula for this component is F = m × g × sin(θ), where m is the mass of the go-cart, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the slope. If we assume the slope makes an angle of θ with the horizontal and the mass of the go-cart is 25 kg, then the force in question A) 245 N would be accurate if the angle of the slope were approximately 14 degrees. Otherwise, we would need the angle of the slope to provide a specific answer.
Part B: Speed at the bottom of the hill
The speed of the go-cart at the bottom of the hill can be calculated using the principle of conservation of mechanical energy, assuming negligible air resistance and no external work done on the system. The initial potential energy converted to kinetic energy at the bottom gives us the equation mg(h + Δy) = ½ m v^2, where m is the mass, g is gravitational acceleration, h is the length of the slope, Δy is the vertical drop, and v is the final velocity at the bottom. Solving for v, the correct answer would be found among the provided options. Yielding a correct speed would require the full slope specifications to be used in the calculations.