ust show a reasonable amount of work to receive full credit - if in doubt, show

Question

ust show a reasonable amount of work to receive full credit - if in doubt, show it! n the following problem, we are ignoring the effects of wind, air pressure, and drag] he height of a projectile at a certain moment is given by the formula h =-16t2 + Vt + s, where t is the umber of seconds the object has traveled, V is the initial vertical speed of the object in feet per second, and s sthe initial height of the object in feet. baseball hits the player's bat 3 feet above home plate, and bounces off the bat at a velocity of 90 mph with n angle of elevation of 26°. The outfield wall is 420 feet from home plate and 10 feet tall. Find the vertical speed V and horizontal speed H of the ball, in feet per second, as it left the bat. Round to two decimal places. (Hint: Use your ideas from page 4! Also, 1 mph = . feet per second) lo fe 4200 118.644/s Scc b. Write the formula for the height of this baseball after t seconds After how many seconds does the ball hit the ground? Use your graphing calculator and round to two decimal places c. d. If there were no obstacles in its way (outfielder,wall, bleachers, etc), how far from home plate would the ball land? Did the player hit a home run? Explain or show work to support your answer. .

Explanation / Answer

given, h = -16.1t^2 + Vt + s

V is the intial vertical speed, s is the initiasl height of object, t is the time in seconds

so, s = 3 feet

theta = 26 deg

V = 90*sin(26) = 39.4534 mph = 57.864 ft/s

distance of outfield wall, d = 420 ft

height of wall, h = 10 ft

a. vertical speed, V = 57.864 ft/s

horizontal speed, v = Vcos(theta) /sin(thetaa) = 57.864/tan(26) = 118.63878ft/s

b. so h = -16.1t^2 + 57.864t + 3

c. so the ball will land when h = 0

-16.1t^2 + 57.864t + 3 = 0

solving for t

t = 3.645 s

d. so hoprizontal distance travelled = vt = 118.638*3.645 = 432.454 ft

e. time taken to reach the wall, t' =?

horizontal distance of the vertical wall, d = 420 ft

so, t' = d/v = 420/118.638 = 3.54 s

height at this point of time, h = -16.1(3.54)^2 + 57.864(3.54) + 3 = 5.0798

this is leeeser thsan the height of the ball, so when the ball crosses the wall, it is at a lower height than the wall, so it strrikes it and falls back into the field

as the ball does nbot go out of the field, the batter did not score a home run

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