Student A is on a 9m Hugh bridge while Student B is on the ground. Student B throws an apple up to Student B with a velocity of 18m/s. How long does it take for the apple to reach student A's hand? if student A is unable to catch the apple, how long would it take for the apple to come back to the ground?

sorry I meant 9m high bridge

a. h = Vo*t + 0.5g*t^2 = 9

18t - 4.9t^2 = 9
-4.9t^2 + 18t - 9 = 0
t=0.597 s. and 3.08 s(Use quad. formula)
Choose t = 0.597 s since the apple reaches its max ht. of 16.5 m, in 1.84 s.

V = Vo + g*t = 0 @ max ht.
18 - 9.8*t = 0
9.8t = 18
Tr = 1.84 s. = Rise time.

b. If student A does not touch the ball it will reach a max ht. of 16.5 m.:

h = 18*1.84 - 4.9*1.84^2 = 16.5 m, max.

Tf = Tr = 1.84 s. = Fall time.

Tr+Tf = 1.84 + 1.84 = 3.68 s. = Time to
return to gnd.

To find the time it takes for the apple to reach student A's hand, we can use kinematic equations and consider the motion of the apple in two parts: its upward motion towards student A and its downward motion back to the ground.

1. Upward motion towards student A:
Let's find the time it takes for the apple to reach its highest point (when it has zero vertical velocity) using the equation:

v = u + at,

where
v = final velocity (0 m/s, since it reaches its highest point)
u = initial velocity (18 m/s)
a = acceleration (acceleration due to gravity, approximately -9.8 m/s^2, negative because it acts in the opposite direction of the velocity)
t = time taken

Rearranging the equation, we get:

t = (v - u) / a.

Substituting the given values, we have:

t = (0 - 18) / -9.8

Simplifying, we get:

t ≈ 1.84 seconds.

2. Downward motion back to the ground:
Since the time taken to reach the highest point is the same as the time taken for the apple to descend back to the ground, it will also take approximately 1.84 seconds for the apple to return to the ground.

So, to summarize:
- The time it takes for the apple to reach student A's hand is approximately 1.84 seconds.
- If student A is unable to catch the apple, it would take approximately 1.84 seconds for the apple to come back to the ground.