OpenResponse Homework Problem 181 A stone is thrown upward f

Open-Response Homework Problem 18.1 A stone is thrown upward from the top of a building at an angle of 35 to the horizontal, with an initial speed of 40 m/s. The building is 50 m tall.

(a)[8 pts] How long does it take for the stone to reach the ground?

(b)[6 pts] What is the speed of the stone the instant before it strikes the ground?

(c)[4 pts] How far from the building (horizontally) does the stone hit the ground?

Solution

a)

V_x=40Cos35=32.766 m/s

V_y=40sin35=22.943 m/s

From

Y_f = Y_i+V_yt + (1/2)at²

=>-50 =0+22.943t+(1/2)(-9.8)t²

4.9t²-22.943t-50=0

t=6.3 s

b)

From

V_yf=V_yi+at =22.943+(-9.8)*6.3

V_yf=-38.8 m/s

V=sqrt[V_x²+V_yf²]=sqrt[32.766²+(-38.8)²]

V=50.8 m/s

c)

distance

D=V_xt =32.766*6.3

D=206.4 m