Answer:
a) 200m, 100m/s
b) 710.20m
c) -117.98 m/s
d) 26.24 s
Explanation:
To solve this we have to use the formulas corresponding to a uniformly accelerated motion problem:
(1)
(2)
(3)
where:
Vo is initial velocity
Xo=intial position
V=final velocity
X=displacement
a)

the intial position is zero because is lauched from the ground and the intial velocitiy is zero because it started from rest.



b)
The intial velocity is 100m/s we know that because question (a) the acceleration is -9.8
because it is going downward.

c)
In order to find the velocity when it crashes, we can use the formula (3).
the initial velocity is 0 because in that moment is starting to fall.

the minus sign means that the object is going down.
d)
We can find the total amount of time adding the first 4 second and the time it takes to going down.
to calculate the time we can use the formula (2) setting the reference at 200m:

solving this we have: time taken= 22.24 seconds
total time is:
total=22.24+4=26.24 seconds.
Answer:
Explanation:
given data= 34.2 m/s
we have to convert it into km/s
as we know that
1 km=1000 m
so 1 m= 1/1000 =0.001 km
now we know that 1 min=60 sec
so 1 sec=1/60= 0.016 min
therefore
34.2m/s = 34.2*m/sec =34.2*0.001 km /0.016 min
so 34.2 m/s =2.1 km/min
Answer:
408.25 Hz.
Explanation:
The fundamental frequency of a stretched string is given as
f' = 1/2L√(T/m') .................... Equation 1
Note: The a steel piano wire is a string
Where f' = fundamental frequency of the wire, L = length of the wire, T = tension on the wire, m' = mass per unit length of the wire.
Given: L = 0.4 m, T = 800 N,
Also,
m' = m/L where m = mass of the steel wire = 3.00 g = 3/1000 = 0.003 kg.
L = 0.4 m
m' = 0.003/0.4 = 0.0075 kg/m.
Substituting into equation 1
f' = 1/(2×0.4)[√(800/0.0075)]
f' = 1/0.8[√(106666.67)]
f' = 326.599/0.8
f' = 408.25 Hz.
Hence the frequency of the fundamental mode of vibration = 408.25 Hz.
1,600 years in an estimate