Homework SourseA stone is thrown from a rooftop at time t0 seconds Its posi
A stone is thrown from a rooftop at time t=0 seconds. Its position at time t is given by r(t)=10ti-5tj+(6.4-4.9t^2)k. The origin is at the base of the building, which is standing on flat ground. Distance is measured in meter.
A). How high is the rooftop and the ground?
B). At what time does the stone hit the ground?
C). How fast is the stone moving when it hits the ground?
D). Where does the stone hit the ground?
E). What is the stone\'s acceleration when it hits the ground?
A). How high is the rooftop and the ground?
B). At what time does the stone hit the ground?
C). How fast is the stone moving when it hits the ground?
D). Where does the stone hit the ground?
E). What is the stone\'s acceleration when it hits the ground?
Solution
a)t=0,r=6.4 k so d=6.4m b)stone hits ground means height=0 6.4-4.9t^2=0 t=1.14s c)v=dr/dt=10i+5j-9.8tk=10i+5j-11.2k v=15.83m/s d)when stone hits ground t=1.14 r=11.4i+5.7j+0k e)a=dv/dt=-9.8k m/s^2
