M1.) Nguyen jumps off a cliff with a height of 100 meters at a velocity of 3.5 meters per second to a save a cat. How long will it take her to reach the surface of the ocean?

A3.) A plane vertically flees a horde of zombies at a speed of 7.9 m/s at a height of 230m above the horde. A man slips out of the plane, how long does he have to grow wings and fly away from the horde of zombies before he falls into the zombies' clutches.

K5.) An archer, shoots an arrow straight upward with a velocity of 90.3 m/s. Captain America is standing 10m to the left of the archer. CA can throw his shield at 50 m/s. When should Captain America throw his shield.

anyone strong in physics, help would be awesome

Assuming the 3.5 m/s is horizontal:

h = 0.5g*t^2.
g = 9.8 m/s^2.
t = ?

A3. h = Vo*t + 0.5g*t^2
h = 230 m.
Vo = -7.9 m/s(plane moving upward).
g = 9.8 m/s^2.
t = ?

K5. The problem doesn't say what the captain is trying to do.

To solve each of these problems, we will use the equations of motion for objects in freefall.

For M1:
The equation we will use here is the equation for the time it takes for an object to fall from a certain height:

t = √(2h/g)

where
t is the time taken to fall,
h is the height of the cliff (100m in this case), and
g is the acceleration due to gravity (approximately 9.8 m/s²).

Plugging in the values, we have:

t = √(2 * 100 / 9.8)
≈ √(20.4)
≈ 4.52 seconds

Therefore, it will take Nguyen approximately 4.52 seconds to reach the surface of the ocean.

For A3:
To solve for the time it takes for the man to fall, we can use the same equation as before:

t = √(2h/g)

In this case,
h is the height of the plane above the horde (230m), and
g is still the acceleration due to gravity (approximately 9.8 m/s²).

Using these values, we have:

t = √(2 * 230 / 9.8)
≈ √(47.04)
≈ 6.86 seconds

So, the man has approximately 6.86 seconds before he falls into the zombies' clutches.

For K5:
In this case, we need to find out when Captain America should throw his shield. Since the archer shoots an arrow straight upward with a velocity of 90.3 m/s, the arrow will reach its highest point before falling back down.

To determine when the arrow reaches its highest point, we can use the equation:

v = u + gt

where
v is the final velocity (0 m/s at the highest point),
u is the initial velocity (90.3 m/s),
g is the acceleration due to gravity (approximately 9.8 m/s²), and
t is the time in seconds.

Rearranging the equation to solve for t, we get:

t = (v - u) / -g
= (0 - 90.3) / -9.8
≈ 9.24 seconds

Therefore, Captain America should throw his shield approximately 9.24 seconds after the archer shoots the arrow.