This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Here are the solutions to the problems: Question 3: a) A child slides up a playground ramp with a speed of 4 m/s. How high up the ramp will the child go? Step 1: Identify the given values and the physical principle. The initial speed (velocity) of the child is v = 4 m/s. We need to find the maximum height h. The acceleration due to gravity is g = 9.8 m/s^2. When the child slides up the ramp, their initial kinetic energy is converted into gravitational potential energy at the maximum height. We use the principle of conservation of mechanical energy: (1)/(2)mv^2 = mgh The mass m of the child cancels out from both sides. Step 2: Rearrange the formula to solve for the height h. (1)/(2)v^2 = gh h = (v^2)/(2g) Step 3: Substitute the given values into the formula and calculate the height. h = (4 m/s)^22 × 9.8 m/s^2 h = 16 m^2/s^219.6 m/s^2 h ≈ 0.82 m The child will go 0.82 m high up the ramp. Question 8: a) A truck of mass 2000 kg moves up a hill at 20 m/s. Find the maximum height reached. Then state whether mass affects the height. Step 1: Identify the given values and the physical principle. The mass of the truck is m = 2000 kg. The initial speed (velocity) of the truck is v = 20 m/s. We need to find the maximum height h. The acceleration due to gravity is g = 9.8 m/s^2. Using the principle of conservation of mechanical energy: (1)/(2)mv^2 = mgh Again, the mass m cancels out from both sides. Step 2: Rearrange the formula to solve for the height h. (1)/(2)v^2 = gh h = (v^2)/(2g) Step 3: Substitute the given values into the formula and calculate the height. h = (20 m/s)^22 × 9.8 m/s^2 h = 400 m^2/s^219.6 m/s^2 h ≈ 20.41 m The maximum height reached by the truck is 20.41 m. Step 4: State whether mass affects the height. As seen in the formula h = (v^2)/(2g), the mass m is not present. This means that for a given initial velocity, the maximum height reached is independent of the mass of the object. No, the mass does not affect the height reached. 3 done, 2 left today. You're making progress.