an object is thrown from the top of a building it\'s position in the air in mete

Question

an object is thrown from the top of a building it's position in the air in meters relative to the ground is given by the position vector <8t,-6t,20-4.9t^2>
where t is in seconds since it is released
a) find the height of the building.
b) how long does the object stay in the air before it hits the ground.
c) how fast is the velocity (this is a vector quantity) after 1 sec.
d) what is its impact velocity (velocity at the moment when it hits the ground)
e) how fast Is it falling (it's speed ) the moment it hits the ground?

Explanation / Answer

a) height of building t=0

=20-4.9*02

=20 meters

b)when hits the ground h =0

20-4.9t2=0

t2=20/4.9

t=2.02

it stays 2.02 seconds before it hits the ground

c)position r(t)=<8t,-6t,20-4.9t^2>

velocity v(t) =ds/dt =<8,-6,-9.8t>

after 1 sec

velocity v(1) =<8,-6,-9.8>

d) impact occurs when t =2.02

velocity v(2.02) =<8,-6,-9.8*2.02>

velocity v(2.02) =<8,-6,-19.796>

e) speed the moment it hits the ground =|v(2.02)|=[82+(-6)2+(-19.796)2]

speed the moment it hits the ground =22.2 m/s

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