A write a set of parameteric equations that describe this si

A. write a set of parameteric equations that describe this situation. x = ______________ y = _______________

B. how long is the ball in the air?

C. how far does the ball travel horizontally?

D. how long does it take the ball to reach maximum height and what was the maximum height?

E. Sketch a graph of the situation on an x-y axis. Be sure to label all key points with (x,y) values and the corresponding time (in seconds). Label axes and show orientation.

Solution

Solution:

(A)

set of parameteric equations that describe this situation. x = 160 cos(45) * t = 160/2 *t

and y = 160/2*t -0.5 *32*t²

y= 160/2 * t -16t²

where g =32 gravitational acceleration in ft/sec²

(B) when final velocity in y direction is 0

v = u +at

0 = 160 sin45 - 32 t

t = 3.53

total time ball reamins in air = 2t = 7.07 sec

(C) total distance travel horizontally = 160cos45 * 7.07 = 800 ft

(D)

when final velcoity is 0 for vertical direction

0 = 160 sin45 - 32 t

t = 3.53

maximum height

h = 160 sin45 * 3.53 - 16*(3.53)²

h= 199.999= 200 ft