An egg is thrown nearly vertically upward from a point near the cornice of a tall building. It just misses the cornice on the way down and passes a point a distance 41.0 m below its starting point at a time 5.00 s after it leaves the thrower's hand. Air resistance may be ignored.
1.What is the initial speed of the egg?
m/s
2.How high does it rise above its starting point?
m
3.What is the magnitude of its velocity at the highest point?
m/s
4.What is the magnitude of its acceleration at the highest point?
m/s2
5.What is the direction of its acceleration at the highest point?
up |
down |
1)Let the maximum height reached by egg ,measured from cornice, be h
let initial speed be 'u'
time taken to reach maximum height =t1= u/g
time taken to fall a height of h+41=5-t1=5-(u/g)
h+41 = 0.5*g*[5-(u/g)]2...(i)
Also, u2=2*g*h=2gh
h=u2/2g...(ii)
Substituting this in (i), we get
(u2/2g)+41 = 0.5*g*[5-(u/g)]2=0.5*g*[25+u2/g2 - 10u/g]=12.5g+0.5u2/g - 5u
Or, 41=12.5g-5u=122.5-5u
u=16.3 m/s
Initial speed pof egg = 16.3 m/s
2) Height point above starting point reached by egg = 16.32/(2*9.8)=13.56m
3)at highest point, velocity is zero
4)Magnitude of accleeration throughout the entire trajectory(including highest point) is =acceleration due to gravity=g=9.8m/s2
5)Direction of accleeration throughout the entire trajectory(including highest point) is vertically downwards
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