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 ?

-Hfinal=hinitial+ vinitial*t -4.9t^2
0=0+10t-4.9t^2 when I solved for t I got .49t.Am I suppose to plug .49t back into the equation?

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?

-For this problem I am suppose to get 9.8m/s and instead got -29.4 m

y = 4.9t - 4.9 t^2. Plug in t = 2s and solve for y.
y(at t=2s) = 9.8 - 4*9.8 = -29.4 m

The first is a quadratic. Either factor it, or use the quadratic equation.

On the second, you cannot get 9.8 m/s as a distance, that is a velocity.

To find the total time it takes for a projectile fired straight up to return to its starting position, we can use the equation of motion:

Hfinal = hinitial + vinitial * t - 4.9t^2

where Hfinal is the final height, hinitial is the initial height (which is usually zero for a vertically straight-up projectile), vinitial is the initial velocity, t is the time, and 4.9 is half of the acceleration due to gravity (in this case, 9.8 m/s^2 divided by 2).

In your case, the initial height is 0 and the initial velocity is 10 m/s. So the equation becomes:

0 = 0 + 10t - 4.9t^2

To find the total time, you need to solve this quadratic equation for t. Since you obtained 0.49t when solving for t, it seems like there might have been an error in your calculations.

To find the correct value of t, you can substitute 0.49t back into the equation and solve for t:

0 = 0 + 10(0.49t) - 4.9(0.49t)^2

Simplifying this equation will give you the correct value of t.

Regarding the second problem, to find how far below the level from which the rock was thrown the rock is 2 seconds later, you can use the same equation:

y = 4.9t - 4.9t^2

Plug in t = 2 seconds and solve for y:

y(at t=2s) = 4.9(2) - 4.9(2)^2

Simplifying this equation will give you the correct value of y, which represents the distance below the level from which the rock was thrown.

It seems like you made an error when evaluating the expression, resulting in a negative value. Double-check your calculations to identify the mistake.