I have a few questions that I need help with and one that needs to be checked please?

t takes 6 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft? (I know I have to use this formual d=vinitial+1/2gt^2, I plug in these numbers d=0+1/2(9.8m/s^2)(6^2 s= 176.4 m, is this right?)

If a projectile is fired straight up at a speed of 10 m/s, the total time to return to its starting position is about (I know I have to use this formula, hfinal=hinitial+vinitial *time+ 1/2gt^2, these are the numbers I plugged in hfinal=0+0*10m/s+1/2(9.8m/s^2(10m/s)^2=490 s, when I suppose to get 2 seconds for my answer.

Ten seconds after starting from rest, an object falling freely downward will have a speed of about ? (I know I have to use this formual vfinal=gt, here is what I plugged in vfinal=(9.8m/s^2)(10 s)=98 m, when I am suppose to get 1000 m/s

A man leans over the edge of a cliff and throws a rock upward at 4.9m/s. How far below the level from which it was thrown is the rock 2 seconds later? ( would the formula I use be d=vt?

Let's check your answers one by one and explain the process to arrive at the correct solutions:

1. The formula for the height of an object in free fall is d = v_initial * t + 1/2 * g * t^2. Plugging in the given values, d = (0) * 6 + 1/2 * 9.8 * (6^2) = 0 + 1/2 * 9.8 * 36 = 176.4 m. So, your calculation is correct.

2. To find the total time it takes for a projectile fired straight up to return to its starting position, we need to use the formula h_final = h_initial + v_initial * t + 1/2 * g * t^2. However, you made a mistake when calculating the final height. The formula should be h_final = h_initial + v_initial * t - 1/2 * g * t^2 (note the minus sign). Plugging in the values, h_final = 0 + 10 * t - 1/2 * 9.8 * (10^2) = 0 + 10t - 1/2 * 9.8 * 100 = 0 + 10t - 490. To find the total time, we set h_final = 0 and solve the equation: 0 = 10t - 490. Rearranging the equation, 10t = 490, and dividing by 10, t = 49 s. Therefore, the correct answer is 49 seconds, not 490.

3. The formula to calculate the final velocity of an object in free fall is v_final = g * t. Plugging in the given value, v_final = 9.8 * 10 = 98 m/s. Therefore, your calculation is correct, and the final velocity is 98 m/s, not 1000 m/s.

4. To find the distance below the level from which the rock was thrown after 2 seconds, we need to use the formula d = v * t. Plugging in the values, d = 4.9 * 2 = 9.8 m. So, your calculation is correct.

I hope this helps clarify the correct answers and the methods used to solve these problems. If you have any additional questions, feel free to ask!