From the top of a cliff with 80 m height a stone is thrown vertically and finally hit the surface of ocean.
Initial velocity of stone is 40 m/s.
Find:
(a) time to reach to max height.
(b) how high goes from surface of ocean?
(c) what is velocity of stone 2 second after thrown?
(d) what is velocity of stone at 20 meters above ocean?
(e) total traveled time?
(f) at what times velocity is 10 m/s?
(g) what is velocity of ball 40 m above ocean?
(h) what is velocity of ball after 6 second from thrown?
(i) at what height from the ocean surface velocity is -50 m/s?
(j) what is velocity of stone just before hit the ocean surface?
I calculated that:
(a) tmax = 4.08 s
(b) ytotal = 161.6 m
(c) vy = 20.4 m/s
(d) vy = 20.4 m/s
(e) ttotal = 9.83 sec
(f) t1 = 3.06 sec ; t2 = 5.1 sec
How would you exactly find g~j? :/
I suppose the variables confuses me a bit.
a. Tr = -Vo/g = -40/9.8 = 4.08 s. = Rise
time.
b. h = ho + (V^2-Vo^2)/2g
h = 80 + (0-(40^2))/-19.6 = 161.6 m.
Above gnd.
c. V = Vo + g*t = 40 - 9.8*2 = 20.4 m/s.
d. V*2 = Vo^2 + 2g*(h-20)
V^2 = 0 + 19.6*(161.6-20) = 2775.36
V = 52.7 m/s.
e. h = 4.9t^2 = 161.6 m.
4.9*t^2 = 161.6
t^2 = 32.979
Tf = 5.74 s. = Fall time.
Tr+Tf = 4.08 + 5.74 = 9.82 s. = Total
time traveled.
f. V = Vo+g*t = 40 - 9.8*t = 10 m/s.
-9.8t = 10-40 = -30
t = 3.06 s.
g. Same procedure as d.
h. V = Vo+g*t = 40 - 9.8*6 = -18.8 m/s.
The negative sign means the stone is falling.
i. h = ho - (V^2-Vo^2)/2g
h = 161.6 - (50^2-0)/19.6 = 34 m.
j. V=Vo + g*Tf = 0 + 9.8*5.74=56.3 m/s
To find the value of "g" in this question, we can use the kinematic equation for vertical motion:
y = y0 + v0y * t - (1/2) * g * t^2
where:
- y is the vertical displacement (in meters)
- y0 is the initial height (in meters)
- v0y is the initial vertical velocity (in meters per second)
- t is the time (in seconds)
- g is the acceleration due to gravity (in meters per second squared)
We know the following values:
- y = 0 (since the stone hits the surface of the ocean)
- y0 = 80 m (initial height)
- v0y = 40 m/s (initial vertical velocity)
- t = 4.08 s (time to reach maximum height)
By substituting these values into the equation above, we can solve for "g". Rearranging the equation, we have:
0 = 80 + 40 * 4.08 - (1/2) * g * (4.08)^2
Simplifying, we get:
0 = 80 + 163.2 - 8.16g
Solving for "g", we have:
8.16g = 243.2
g ≈ 29.84 m/s^2
So, the value of "g" in this case is approximately 29.84 m/s^2.