Projectile motion? Need to solve Graphically?

Question

Hitting a baseball
-A baseball is hit when it is 4 ft above the ground. It leaves the bat with an initial velocity of 155 ft/sec, making an angle of 18 with the horizontal. At the instant he ball is hit, an instantaneous 11.7 ft/sec gust of wind bloes in the horizontal direction against the ball, adding a component of -11.7i to the ball’s initial velocity. A 10-foot-high fence is 380 ft from homeplate in the direction of the flight.

b) How high does the baseball go, and when does it reach maximum height?
c) Find the range and flight time of the baseball.
d) When is the baseball 25 ft high? How far (ground distance) is the baseball from home plate at that height?

I need help plotting the problem in a graphing calculator. What mode or function do i use, how can i find the intercepts. Please help me or guide me in how to use the graphing calculator. Thank you

Answer 1

The x and y components of the baseball at any time t is given by the following parametric equations:
x = (Vo*cos z)t and y = -.5gt^2 +(Vo*sin z)t, where:
Vo = initial velocity
z = angle of inclination
g = the gravitational constant
t = time in seconds.

Eliminating t, gives:
y = -gx^2/(Vocos^2z) +xtan z

You say "At the instant the ball is hit, an instantaneous 11.7 ft/sec gust of wind blows in the horizontal direction against the ball, adding a component of -11.7i to the ball’s initial velocity. So I guess this means that the initial velocity is changed from 155ft/sec at angle z to some other value at some other angle. Is this correct?

Also, you should add 4 to y to account for the ball starting 4 feet off the ground.

I leave the rest of the solution up to you because I do not know the exact effect of the instantaneous gust of wind on the trajectory of the ball. If it is instantaneous (has no significant duration), then I'm not sure it affects the inclination angle, but, I think it does affect the initial speed.

Anyhow, this should be sufficient data to let you solve the problem.

Answer 2

Confusing:
a) you said the when leaving the bat has a velocity of 155 ft/sec - is this the true velocity ?
If this is the real given then the problem can be solved.
b) the space here for the solution is limited,
c) I don't have the calculator with graphics, mine is Casio Fx602
. . . no graphics
My solution
Vx =155cos18-11.7 = 135.51
Vy = 155sin18=47.90
time in reaching the fence = 380 / 135.51 = 2.80 sec
height of ball on fence = 47.9(2.8)-9.81/2(2.8)^2 = 95.66
vertical clearance =95.66-6 =89.66 very high

When reaching the ground
-4 = 47.9 t - 9.81/2 t^2 . . . . t = 9.85

its really too long solution
I give up

Answer 3

It depends on your calculator brand.