Vertical Motion (1 Viewer)

[Da_Bomb]

A body is let fall from a height of 150m. What is its height and velocity after falling freely for 5 seconds.


And


A stone is let fall from a tall building and 1 second later another stone is projected vertically downwards with a velocity of 20m/s. When will the second stone overtake the first. ?

 

[madbandlt]

1) s = ut + 1/2at^2

u = 0 (initial velocity being 0)
t = 5 (given)
a = -9.8 (gravitational acceleration)

s = 0--4.9(25)
s = -122.5

Therefore 150 - 122.5 = 27.5m

then v = u + at
v = 0 - 9.8(5)
v = -49m/s



2) 1st Stone
u = 0
a = -9.8 m/s
s = -4.9t^2 (derive yourself) Equation 1


2nd Stone
u = -20m/s
a = -9.8 m/s
s = -20T - 4.9T^2 (again derive yourself) Equation 2


Now, the second stone is released 1 second AFTER the 1st stone. Hence you sub in T = t -1

s = -20(t-1) - 4.9(t-1)^2

After simplifying and collecting like terms...

s = -4.9t^2 - 10.2t + 15.1

Now we use simultaneous equations

-4.9t^2 = -4.9t^2 - 10.2t +15.1
10.2t = 15.1

t = 1.48 seconds (2 d.p)






BTW, we have a topic test next week

 

[Da_Bomb]

Thanx man

 

[cutemouse]

this is maths, not physics, and i'm afraid you would get zero marks for that answer in a maths exam. You are not permitted to use physics formulae (unless you want to prove them first). You are expected to use calculus.

+1