Jake serves a volleyball with an initial velocity of 32 feet per second from 4.5 feet above the ground at an angle 0f 35 degrees.
a) Write parametric equations to model the situation.
b) How far will the ball travel( if it hits the ground)show work
Vo = 32Ft/s[35o]
Xo = 32*cos35 = 26.21 Ft/s.
Yo = 32*sin35 = 18.35 Ft/s.
a. Y = Yo + g*Tr = 0 @ max. ht.
Tr=(Y-Yo)/g = (o-18.35)/-32.4=0.566 s
= Rise time or time to reach max. ht.
hmax = ho + Yo*t + 0.5g*Tr^2
hmax = 4.5 + 18.35*0.566 - 16.2*0.566^2 = 9.70 Ft above gnd.
b. hmax = 0.5g*t^2 = 9.70 Ft.
16.2*t^2 = 9.70
t^2 = 0.599
Tf = 0.7740 s. = Fall time or time to
fall to gnd.
Range = Xo * (Tr+Tf)
Range = 26.21 * (0.566+0.774) = 35.12 Ft