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.
For a question this long, you really need to show some work of your own. You certainly can compute the time it takes the ball to reach the batter. (Part a)
i don't see why a home run should have to clear the fence by one foot (unless an outfielder can reach a foot higher than the fence)
Your first job in (b) is to calculate the velocity of the batted ball that is required to clear the fence by one foot. Use 32.2 ft/s^2 for g.
I have noooooo idea where to start.. this isn't even for a grade.. it was a free response on a test i got back.
Looks more like a long question than a response to one.
whatever you want to call it; it was 1/3 of the test.
a) To find the reaction time, we need to calculate the time it takes for the ball to travel the distance from the pitcher to the batter. We can use the formula for time:
time = distance / velocity
In this case, the distance is the same as the distance between the pitcher and the batter, d, and the velocity is given as 95 mph. However, we need to convert the velocity from mph to ft/s as follows:
95 mph * (5280 ft / 1 mi) * (1 mi / 60 min) * (1 min / 60 s) = velocity in ft/s
Once we have the velocity in ft/s, we can calculate the reaction time by dividing the distance by the velocity.
b) To determine the minimum percentage of pitch velocity that must be transferred to the ball for a homerun, we need to consider the energy the ball needs to clear the fence. We can break this down into two parts: the kinetic energy required and the potential energy gain.
The kinetic energy (KE) required to clear the fence can be calculated using the equation:
KE = (1/2) * mass * velocity^2
To find the minimum percentage of pitch velocity that must be transferred to the ball, we can compare the initial velocity of the pitch to the final velocity of the ball when it clears the fence.
c) To find the maximum height attained by the homerun ball, we can consider the projectile motion of the ball after it is hit. Since we know the initial angle of the ball, we can use the equations of motion to find the maximum height (vertex) reached by the ball.
d) To determine how long it took for the homerun ball to clear the wall, we can calculate the time it takes for the ball to reach its highest point (the vertex) using the equations of motion.
e) To find the total distance traveled by the homerun ball, we need to consider the horizontal distance it covers. We can calculate the horizontal distance using the initial velocity, initial angle, and time of flight.