I posted this question before and i really need help on it...

A pitcher throws a baseball to a batter at 95 mph from a distance, d, away. The batter swings and hits the ball. (5280 ft = 1 mi, g = 32.174 ft/s/s).

a) Assuming the pitch travels the full distance, d, how much reaction time does the batter have to hit the ball?
b) What minimum percentage of pitch velocity much be transferred to the ball for the batter to hit a homerun? Assume the point where it clears the fence is 395 ft away and the fence at this point is 12 ft high. For the ball to clear the fence, assume it has to be at least 1 ft higher than the fence at the time it passes over the fence. Also assume the pitch was waist high, 3 ft from the ground, when it was hit and made an initial angle of 35° with the ground.
c)what is the maximum height that the homerun ball attained?
d) How long did it take for the homerun to clear the wall?
e) How far did the homerun travel in total? Assume that there is no fan interference. Assume the height of the ball at this point is the same as the height of the ground.

To answer these questions, we need to use some physics formulas and equations. Let's break down each part of the problem step by step.

a) To find the reaction time of the batter, we need to calculate the time it takes for the pitch to reach the batter. We can use the formula: time = distance / velocity.

Given:
- Pitch velocity: 95 mph
- Distance from pitcher to batter: d

First, we need to convert the pitch velocity from miles per hour (mph) to feet per second (ft/s) since the other units are in feet.

Conversion:
- 1 mile = 5280 feet
- 1 hour = 60 minutes = 60 seconds

So, 95 mph = 95 * 5280 ft / (60 min * 60 sec) = 139.33 ft/s (approximately)

Now, we can calculate the reaction time:
time = d / 139.33 ft/s

b) To find the minimum percentage of pitch velocity that must be transferred to the ball for a homerun, we need to consider the energy transfer. The ball's potential energy at its maximum height must be enough to clear the fence.

Given:
- Distance to clear the fence: 395 ft
- Fence height: 12 ft
- Initial angle of the pitch: 35°
- Pitch height: 3 ft

First, let's calculate the initial velocity of the pitch using the horizontal component of its speed. We can use the formula: velocity = pitch velocity * cos(angle).

velocity = 95 mph * cos(35°) = 95 * 0.8192 ≈ 77.79 ft/s

Now, let's calculate the minimum speed required for the ball to clear the fence. The ball's maximum height can be found using the formula: height = (initial velocity^2 * sin^2(angle)) / (2 * acceleration), where acceleration is gravitational acceleration (g).

height = (77.79^2 * sin^2(35°)) / (2 * 32.174 ft/s^2)

To clear the 12 ft fence, the minimum height of the ball should be 12 + 1 = 13 ft. Now we can solve for the minimum speed.

(77.79^2 * sin^2(35°)) / (2 * 32.174 ft/s^2) = 13 ft

From here, we can solve for the minimum percentage of pitch velocity needed.

c) To find the maximum height of the homerun ball, we've already calculated it in part b) as "height".

d) To determine how long it took for the homerun ball to clear the wall, we need to calculate the time taken to reach the maximum height. We can use the formula: time = velocity / acceleration.

Given:
- Initial vertical velocity (upward): vertical component of the pitch velocity * sin(angle)

Now, use the formula:
time = vertical velocity / g

e) Lastly, to find the total distance traveled by the homerun ball, we need to calculate the horizontal range it covers. We can use the formula: range = time * velocity.

Given:
- time: calculated from part d)
- velocity: pitch velocity

Now, use the formula:
range = time * velocity

This should help you solve the problem step by step. Make sure to double-check the calculations and units to get accurate answers.

a) To find the reaction time of the batter, we need to determine the time it takes for the pitch to reach the batter. The formula to calculate time is t = d/v, where t is the time, d is the distance, and v is the velocity.

Given that the pitch travels at 95 mph, we need to convert this to feet per second. Since 1 mile = 5280 feet and 1 hour = 3600 seconds, we can convert mph to ft/s by multiplying by (5280/3600).

95 mph * (5280 ft/mi) / (3600 s/h) = 139.33 ft/s (approx)

Now we can calculate the reaction time by dividing the distance (d) by the velocity (v).

Reaction time = d / v

b) To determine the minimum percentage of pitch velocity that must be transferred to the ball for the batter to hit a homerun, we need to consider the distance and height of the fence.

Given that the point where the ball clears the fence is 395 ft away and the fence is 12 ft high, we can determine the initial velocity of the ball when it leaves the bat using the range formula.

Range = (v^2 * sin(2θ)) / g

Where v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

Since the pitch was hit waist high, 3 ft from the ground, we need to calculate the initial velocity using the launch angle of 35°. Rearranging the formula, we have:

v = sqrt((Range * g) / sin(2θ))

Given that the range is 395 ft, the launch angle is 35°, and g is 32.174 ft/s^2, we can calculate the initial velocity of the ball.

Minimum percentage = (v / 139.33 ft/s) * 100

c) To determine the maximum height that the homerun ball attained, we can use the projectile motion formula for the vertical displacement:

Δy = v^2 * sin^2(θ) / (2g)

Given that the launch angle is 35°, and the initial velocity v is obtained from the previous calculation, we can calculate the maximum height attained by substituting these values into the formula.

d) To find the time it took for the homerun ball to clear the wall, we need to determine the time it took for the ball to reach the fence and go beyond it.

First, we calculate the time it takes to reach the maximum height using the formula:

t = vy / g

where vy is the vertical component of the initial velocity. Then, we double the time to account for both the ascent and descent phases. Since the ball will be at the same height as the ground when it clears the wall, we know the time it takes for the ball to reach the ground:

t_total = 2 * t

e) Finally, to find the total distance travelled by the homerun ball, we can use the range formula once again, considering the time it took for the ball to clear the wall:

Total distance = v_total * t_total

Substituting the values for velocity and time calculated above, we can find the total distance travelled by the homerun ball.