Final answer:
The speed of the mass at heights of 300 m, 200 m, and 100 m above the ground can be calculated using the equations of motion and the acceleration due to gravity. The speeds are found to be 31.36 m/s, 22.14 m/s, and 14.00 m/s respectively. As the mass hits the ground, its speed is found to be 64.02 m/s.
Step-by-step explanation:
To find the speed of the mass as it reaches different points, we can use the equations of motion. First, let's find the speed of the mass at a height of 300 m. We can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Since the mass is falling freely, acceleration due to gravity can be used as the acceleration term. Taking the initial velocity as zero, we can calculate the speed at a height of 300 m using the equation v^2 = 0 + 2 * 9.8 * (325 - 300). Solving this equation, we find the speed to be 31.36 m/s.
Similarly, we can calculate the speeds at heights of 200 m and 100 m using the same equations. At a height of 200 m, the speed is found to be 22.14 m/s, and at a height of 100 m, the speed is found to be 14.00 m/s. Finally, to find the speed as the mass hits the ground, we can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. In this case, the displacement is 325 m, the acceleration is gravity, and the initial velocity is zero. Solving this equation. we find the final velocity or the speed to be 64.02 m/s.