Here\'s a homework question I just can\'t solve: A baseball player hits a baseba
ID: 2894710 • Letter: H
Question
Here's a homework question I just can't solve: A baseball player hits a baseball 3 ft above the ground toward the center field fence, which is 11 ft high and 400 ft from home plate. The ball leaves the bat with a speed of 115 ft/s at an angle 50° above the horizontal.
A:) Does the ball go over the fence for a home run? (Use g = 32 ft/s2.)
B:) How high is the ball above the ground when it reaches the fence? (Give your answer correct to at least one decimal place.)
*I care more about the answer to part B, I got part A right (which was yes it does).
Explanation / Answer
let position =s , velocity=v , acceleration =a
x coordinate is horizontal component , y coordinate is vertical component
a(t)= <0,-32>
v(t)=(a(t)) dt
v(t)=<0,-32> dt
v(t)=<0,-32t>+c
v(0)=<115cos50o,115sin50o>
<0,-32*0>+c=<115cos50o,115sin50o>
<0,0>+c=<115cos50o,115sin50o>
c=<115cos50o,115sin50o>
v(t)=<0,-32t>+<115cos50o,115sin50o>
v(t)=<115cos50o,-32t+115sin50o>
s(t)=v(t) dt
s(t)=<115cos50o,-32t+115sin50o> dt
s(t)=<(115cos50o)t,-16t2+(115sin50o)t> +d
s(0)=<0,3>
<(115cos50o)*0,-16*02+(115sin50o)*0> +d=<0,3>
=> <0,0>+d=<0,3>
=> d=<0,3>
s(t)=<(115cos50o)t,-16t2+(115sin50o)t> +<0,3>
s(t)=<(115cos50o)t,-16t2+(115sin50o)t +3>
fence is 400 ft from home plate
for time taken by ball to reach fence
=>(115cos50o)t=400
=>t=400/(115cos50o)
=>t=5.411sec
height of the ball above the ground when it reaches the fence =(-16*5.4112)+((115sin50o)*5.411) +3
height of the ball above the ground when it reaches the fence =11.2 feet