please help i cannot figure this out

A 0.27 kg ball of dough is thrown straight up into the air with an initial velocity of 12 m/s.
Find the momentum of the ball of dough halfway to its maximum height on the way up.
and

A 61 kg pole-vaulter falls from rest from a height of 6.6 m onto a foam-rubber pad. The pole-vaulter comes to rest 0.30 s after landing on the pad.
Calculate the athlete's velocity just before reaching the pad.
Calculate the constant force exerted on the pole-vaulter due to the collision.

To find the momentum of the ball of dough halfway to its maximum height, we first need to find the height reached by the ball of dough when it is halfway to its maximum height.

The maximum height reached by the ball of dough can be determined using the equation for vertical motion:

h = (v^2 - u^2) / (2*g)

where:
h = maximum height
v = final velocity (which is 0 m/s at the maximum height)
u = initial velocity
g = acceleration due to gravity (approximately 9.8 m/s^2)

Substituting the given values into the equation, we have:
u = 12 m/s
v = 0 m/s
g = 9.8 m/s^2

h = (0^2 - 12^2) / (2 * 9.8)
h = (-144) / 19.6
h ≈ -7.347 m/s

Since the height cannot be negative, the ball of dough reaches a maximum height of approximately 7.347 meters.

Halfway to the maximum height would be at 7.347/2 = 3.674 meters.

Now, momentum is defined as the product of an object's mass and its velocity. Therefore, to find the momentum halfway to the maximum height, we need to calculate the velocity of the ball of dough at that point.

We can use the equation for vertical motion:

v = u - g*t

where:
v = final velocity
u = initial velocity
g = acceleration due to gravity
t = time

Since we are halfway to the maximum height, the time would be half the time it takes to reach the maximum height.

The time it takes to reach the maximum height can be determined using the equation:

v = u - g*t

0 = 12 - 9.8*t
9.8*t = 12
t = 12 / 9.8
t ≈ 1.224 s

Therefore, halfway to the maximum height, the time would be t/2 = 1.224 / 2 = 0.612 s.

Substituting these values into the equation for velocity:

v = 12 - 9.8 * 0.612
v ≈ 12 - 5.9856
v ≈ 6.0144 m/s

Now we can calculate the momentum:

momentum = mass * velocity

Given that the mass is 0.27 kg and the velocity is 6.0144 m/s, we can calculate:

momentum = 0.27 * 6.0144
momentum ≈ 1.6246 kg*m/s

Therefore, the momentum of the ball of dough halfway to its maximum height on the way up is approximately 1.6246 kg*m/s.

For the second problem, we need to find the athlete's velocity just before reaching the pad and the constant force exerted on the pole-vaulter due to the collision.

To find the velocity, we can use the equation of motion:

v = u + a*t

where:
v = final velocity (which we need to find)
u = initial velocity (which is 0 m/s as the pole-vaulter falls from rest)
a = acceleration (we need to find this)
t = time (given as 0.30 s)

The acceleration can be determined using the equation:

a = (v - u) / t

Since we are solving for v, we can rearrange the equation:

v = u + a*t

Now, when the pole-vaulter reaches the pad, the final velocity is 0 m/s. Hence, we have:

0 = 0 + a * 0.30
a * 0.30 = 0
a = 0 / 0.30
a = 0 m/s^2

Hence, the acceleration is 0 m/s^2.

Now, we can use the equation:

v = u + a*t

Substituting the given values:

v = 0 + 0 * 0.30
v = 0 m/s

Therefore, the athlete's velocity just before reaching the pad is 0 m/s.

To calculate the constant force exerted on the pole-vaulter due to the collision, we can use Newton's second law of motion:

F = m * a

where:
F = force (which we need to find)
m = mass (given as 61 kg)
a = acceleration (which we found to be 0 m/s^2)

Substituting the known values:

F = 61 * 0
F = 0 N

Hence, the constant force exerted on the pole-vaulter due to the collision is 0 Newtons.