posted by Raye
A baseball is hit by Aaron Judge, a New York Yankees baseball team member, at an amazing velocity of 110 miles/hour at an angle of 35 degrees from the horizontal from home plate in Yankee Stadium in New York City. The baseball was initially launched from an elevation of 4 feet above ground. The distance from home plate to the outfield wall is 408 feet at center field. The height of the outfield wall is approximately 8 feet (It varies slightly across the outfield). You should first draw a two-dimensional picture of the baseball’s trajectory (x, y coordinate system) to assist in developing answers to the questions below. Note: Convert all variables to the metric (mks) system before performing your calculations.
b)What is the maximum height reached by the ball?
c)What is the total time of flight?
No I will not use miles and feet
49.2 meters/sec = 110 mph
u = horizontal speed = 49.2 cos 35 = 40.3 m/s
that is constant
x = 40.3 t
v = Vi - 9.81 t
Vi = 49.2 sin 35 deg = 28.2 m/s
v = 28.2 -9.81 t
at top, v = 0
so t = 2.87 seconds to top
h = top = Hi + Vi t - 4.9 t^2
Hi = 4 feet = 1.22 meters
h = 1.22 + 28.2(2.87)-4.9(2.87)^2
h = 1.22 + 80.9 - 40.4
= 41.7 meters at top
when does it reach 8 feet?
2.44 = 1.22 + 28.2 t -4.9 t^2
solve quadratic for t
use range = u*t to see if it cleared the wall
if it did solve for t at h = 0